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Title: Delay-dependent robust control for nonlinear time-delay systems : analysis, synthesis, and application
Other Titles: Fei xian xing shi zhi xi tong de shi zhi xiang guan lu bang kong zhi : fen xi, zong he ji ying yong
非綫性時滯系統的時滯相關魯棒控制 : 分析, 綜合及應用
Authors: Chen, Cailian (陳彩蓮)
Department: Dept. of Manufacturing Engineering and Engineering Management
Degree: Doctor of Philosophy
Issue Date: 2006
Publisher: City University of Hong Kong
Subjects: Robust control
Time delay systems
Notes: CityU Call Number: TJ217.2.C485 2006
Includes bibliographical references (leaves [205]-222)
Thesis (Ph.D.)--City University of Hong Kong, 2006
xiii, 226 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: Nonlinear time-delay systems (NTDS) represent a large class of infinite-dimensional systems used to describe propagation, transport phenomena and population dynamics, etc. The delay effect on stability and performance of control systems is a problem of recurring interest since the presence of delay may induce complex behaviors, especially for nonlinear systems. One of the central problems is how to integrate the nonlinear structural information and delay information to facilitate the analysis and synthesis of control systems. This Thesis initiates a systematic investigation into the stability analysis and control synthesis and provides some rigorous delay-dependent computational methodologies. Firstly, we consider a class of NTDS described by the time-delay Takagi-Sugeno (T-S) fuzzy model. This model consists of a number of local linear time-delay dynamics in each fuzzy implication. With this structural property, some sufficient conditions and an upper bound of the delay are derived to ensure that the system is asymptotically stable for any delay not greater than this upper bound. A novel fuzzy dynamic output feedback controller is designed by using a proposed Generalized Parallel Distributed Control method and robust optimization technique. Secondly, the time-delay piecewise linear (TDPWL) model is used to describe another class of NTDS with abrupt changes of system dynamics. In this Thesis, various kinds of piecewise controllers are proposed based on a Lyapunov-Krasovskii Functional (LKF) together with the structural properties of the TDPWL systems. Then these results are further developed for time-delay T-S fuzzy systems via a novel piecewisefuzzy space partition method. It is shown that the utilization of the structural information in the LKF and partition method reduces the conservatism of the obtained delay-dependent stability and stabilization conditions. The advantages of the proposed approaches over the existing methods are shown by some convincing examples. This Thesis also presents a study on sliding mode control for systems with timedelay inputs subject to un-matched uncertainties. A new coordinate transformation method is proposed so that new invariant conditions for sliding modes can be formulated. A novel controller is then constructed to ensure exponential convergence of both the motions of the sliding surfaces and the dynamics of the reduced-order system on the surfaces. Finally, we present some results on chaos synchronization and stabilization problems based on the delayed feedback control (DFC) method which is considered as an application of delay. Particular attention is focused on the synchronization methods under a master-slave framework with propagation delays in the communication channel. It is observed in this Thesis that this synchronization setting may be recast as a more general DFC structured synchronization problem. Several DFC based synchronization methods are then proposed for non-delay and time-delay chaotic systems. Unlike existing methods where the controller delays are mostly chosen by trial-and-error, the controller gains and an upper bound of the time-delay controller can be simultaneously determined by the proposed technique.
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