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Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems 被引量:5
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作者 Saliha Marir Mohammed Chadli 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第3期685-692,共8页
This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict... This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods. 展开更多
关键词 CONTROL FRACTIONAL-ORDER systems linear matrix inequalities (LMIs) output feedback CONTROL robust ADMISSIBILITY SINGULAR systems UNCERTAIN systems
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Adaptive fault-tolerant control of linear time-invariant systems in the presence of actuator saturation 被引量:2
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作者 Wei GUAN Guanghong YANG 《控制理论与应用(英文版)》 EI 2009年第3期321-327,共7页
This paper studies the problem of designing adaptive fault-tolerant controllers for linear tirne-invariant systems with actuator saturation. New methods for designing indirect adaptive fault-tolerant controllers via s... This paper studies the problem of designing adaptive fault-tolerant controllers for linear tirne-invariant systems with actuator saturation. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updating automatically to compensate the fault effects on systems. The designs are developed in the framework of linear matrix inequality (LMI) approach, which can enlarge the domain of attraction of closed-loop systems in the cases of actuator saturation and actuator failures. Two examples are given to illustrate the effectiveness of the design method. 展开更多
关键词 Actuator saturation linear systems Adaptive control Fault-tolerant control Domain of attraction LMIS
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Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems
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作者 Peter Chang-Yi Weng Frederick Kin Hing Phoa 《Advances in Pure Mathematics》 2020年第4期155-173,共19页
In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-tim... In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods. 展开更多
关键词 CONTINUOUS-TIME linear time-invariant system Condition Number PERTURBATION BOUND RICCATI Differential EQUATION CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATION
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Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems
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作者 Babak Esmaeili Hamidreza Modares 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第9期1918-1932,共15页
This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)syste... This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach. 展开更多
关键词 Data-driven control linear parameter-varying systems probabilistic control safe control
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Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems
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作者 曾庆山 曹广益 朱新坚 《Journal of Shanghai Jiaotong university(Science)》 EI 2004年第2期20-24,共5页
The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and n... The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems. 展开更多
关键词 fractional calculus fractional-order linear time-invariant systems CONTROLLABILITY OBSERVABILITY STABILITY
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COMPREHENSIVE DAMPING COEFFICIENT——A NEW DEFINITION TO DAMPING EFFECT OF LINEAR TIME-INVARIANT SYSTEMS
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作者 李先彬 安立进 《Science China Mathematics》 SCIE 1989年第12期1511-1520,共10页
A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D(... A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D(X_0, X)=Ci∫_(x_0, x) x_idx_(i-1)and comprehensive damping coefficient η-min(Ci/a_(n-i)). It is concluded that (ⅰ) of the Hurwitz determinants, △_(x-1) is proportional to the damping effect of oscillating systems, (ⅱ) the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and (ⅲ) the damping torque coefficient obtained for synchronous machines is independent of ω. 展开更多
关键词 LYAPUNOV THEOREM HURWITZ DETERMINANT linear time-invariant system.
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The identification algorithm for commensurate order linear time-invariant fractional systems
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作者 王振滨 曹广益 朱新坚 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2005年第5期576-580,共5页
An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at... An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned. 展开更多
关键词 fractional systems COMMENSURATE linear time-invariant state-space representation system identification
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The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation
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作者 Daniel A. Jaffa 《Journal of Applied Mathematics and Physics》 2024年第1期98-125,共28页
Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of ... Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation. 展开更多
关键词 Hessian Matrices Jacobian Matrices Laplace Equation linear Partial Differential Equations systems of Partial Differential Equations Harmonic Functions Incompressible and Irrotational Fluid Mechanics
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Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning
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作者 Adolfo Perrusquía Weisi Guo 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第1期90-102,共13页
Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior lear... Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach. 展开更多
关键词 Experience inference hippocampus learning system linear time-variant(LTV)systems neocortex/striatum learning systems nonlinear systems optimal control
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Group-Consensus of Hierarchical Containment Control for Linear Multi-Agent Systems
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作者 Jingshu Sang Dazhong Ma Yu Zhou 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第6期1462-1474,共13页
The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection a... The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then,under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol. 展开更多
关键词 Group-consensus behavior hierarchical containment control linear multi-agent systems three-layer topology
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Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems
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作者 Bo Wu Xingbao Gao 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1601-1615,共15页
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun... This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method. 展开更多
关键词 Block triangular splitting Block two-by-two linear systems Eigenvalues PRECONDITIONER flexible generalized minimal residual(FGMRES)
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Event-Triggered Finite-Time H Filtering for Discrete-Time Nonlinear Stochastic Systems
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作者 Aiqing Zhang Yunyuan Dong 《Journal of Applied Mathematics and Physics》 2023年第1期13-21,共9页
This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-K... This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H<sub>∞</sub> filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H<sub>∞</sub> filter gain matrices can be expressed in an explicit form. 展开更多
关键词 Event-Triggered Scheme Discrete-Time Nonlinear Stochastic systems Stochastic Finite-Time Stable linear Matrix Inequalities (LMIS)
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Compressive Measurement Identification of Linear Time-Invariant System Application in DC Motor
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作者 Peng Qiu Qian Dong +2 位作者 Mingqian Li Guangjie Zhai Xueyan Wang 《Journal of Beijing Institute of Technology》 EI CAS 2019年第3期399-409,共11页
In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal proces... In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal processing, a signal with N elements must be sampled at least N times. Thus, most SI methods use N or more sample data to identify a model with N parameters;however, this can be improved by a new sampling theory called compressive sensing (CS). Based on CS, an SI method called compressive measurement identification (CMI) is proposed for reducing the data needed for estimation, by measuring the parameters using a series of linear measurements, rather than the measurements in sequence. In addition, the accuracy of the measurement process is guaranteed by a criterion called the restrict isometric principle. Simulations demonstrate the accuracy and robustness of CMI in an underdetermined case. Further, the dynamic process of a DC motor is identified experimentally, establishing that CMI can shorten the identification process and increase the prediction accuracy. 展开更多
关键词 system IDENTIFICATION (SI) COMPRESSIVE sensing (CS) signal MEASUREMENT linear time-invariant (LTI) system
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Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI 被引量:3
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作者 马合保 秦超英 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第2期57-65,共9页
This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of... This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs. 展开更多
关键词 descriptor linear systems static output feedback H control linear matrix inequality.
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ADAPTIVE TRACKING CONTROL FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS *
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作者 姜斌 万健如 +1 位作者 王先来 王江 《Transactions of Tianjin University》 EI CAS 1998年第1期88-91,共4页
In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonli... In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method. 展开更多
关键词 nonlinear large scale systems adaptive tracking control input output linearization
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ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL
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作者 姜斌 万健如 王先来 《Transactions of Tianjin University》 EI CAS 1999年第1期42-46,共5页
The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (... The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique. 展开更多
关键词 nonlinear interconnected systems UNCERTAINTY STABILIZATION variable structure control input/output linearization
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使用《Linear Control Systems Engineering》的实践
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作者 王林江 徐德胜 +1 位作者 康海珍 顾秀芳 《电气电子教学学报》 2004年第1期30-31,97,共3页
本文介绍了使用原版教材《L inear Con trol Systems Engineering》、英语授课的教学实践及改革措施 ,提出了进一步的实施计划。
关键词 高校 linear Control systems Engineering》 原版教材 英语授课 教学改革 现代控制理论
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Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty 被引量:11
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作者 Jian-Min Jiao 《International Journal of Automation and computing》 EI 2012年第1期8-15,共8页
The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for... The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach. 展开更多
关键词 Discrete singular systems time-varying delay linear fractional uncertainty robust stability robust stabilization linear matrix inequality (LMI).
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Global stabilizing controller design for linear time-varying systems and its application on BTT missiles 被引量:8
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作者 Tan Feng Duan Guangren 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第6期1178-1184,共7页
A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved b... A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance. 展开更多
关键词 linear time-varying systems global stability gain-scheduled control eigenstructure assignment BTT
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BLOCK DIAGONAL FORM AND BLOCK DIAGONAL CONTROLLER OF NONLINEAR SYSTEMS 被引量:5
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作者 Zhao Guorong Zhang Fuen(Dept. of Automatic Control, Harbin Institute of Technology, Harbin, China, 150001)Gu Wenjing(Naval Aeronautical Engineering Academy, Yantai, Shantong, China, 264001) 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1997年第1期51-57,共7页
A block diagonal form about a nonlinear system is defined. Based on the de finition, a design method ca1led block diagonal controller (BDC) is proPOsed bo feedbacklinearization. Thus, a linearization design of a class... A block diagonal form about a nonlinear system is defined. Based on the de finition, a design method ca1led block diagonal controller (BDC) is proPOsed bo feedbacklinearization. Thus, a linearization design of a class of nonlinear system can be simply re-alized. The result of design has been proved by mathematical simulation of a certain anti-ship missile. 展开更多
关键词 feedback linearIZATION nonlinear systems flight control controllers
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