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Robust Control of Uncertain Switched Linear Discrete Time Systems with Time Delays
Author: FuMeiChun
Tutor: ZhangNi；YuLi
School: Zhejiang University of Technology
Course: Control Theory and Control Engineering
Keywords: switched system timedelay robust control guaranteed cost control H_∞control piecewise quadratic Lyapunov functions
CLC: TP13
Type: Master's thesis
Year: 2009
Downloads: 140
Quote: 2
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Abstract
As a special class of hybrid systems, the switched systems are composed of a family of subsystems and a rule orchestrating the switching between the subsystems. With the development of science and technology, the problems encountered in many fields should be resolved by switched system theory.The Analysis and control of the switched systems become very difficult when time delays and uncertainties exist in real systems. Hence the study on robust control of uncertain switched systems with time delays is of great significance.This dissertation investigates the robust control of the switched linear discrete time systems with time delays. The main contributions of this dissertation are as follows.(1) The guaranteed cost control problem of the uncertain switched discrete time systems with delayed states and inputs is discussed for the quadrautic performance index. Based on the piecewise quadratic Lyapunov functions, the synthesis method of the guaranteed cost controllers with statebased switching law is developed. By the obtained control law, the perturbed switched discrete time systems can be asymptotically stabilized and the close loop cost is not greater than a specified upper limit for all admissible uncertainties.(2) By considering the controller perturbation, the nonfragile guaranteed cost control problem of the uncertain switched discrete time systems with multidelays in states and inputs is discussed for the quadratic cost functions. Based on the piecewise quadratic Lyapunov functions, the synthesis method of the delaydependent nonfragile guaranteed cost controllers with statebased switch law is proposed. Then a cone complementarity linearization algorithm is used to solve the nonlinear matrix inequalities. By the obtained control law, the perturbed switched discrete time systems can be asymptotically stabilized and the close loop cost is not greater than a specified upper limit for all admissible uncertainties.(3) Due to the existence of the controller parameter uncertainties, the nonfragile robust H_∞. control problem is investigated for the polytopically uncertain switched discrete time systems with multiple state and input delays. The synthesis approach of the delaydependent nonfragile H_∞controllers with statebased switch law is presented. The nonlinear matrix inequality involved in the controller design is transformed into nonlinear programming problem constrained by nonlinear matrix using a cone complementarity linearization algorithm.

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