Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Cybernetics ( control theory, mathematical theory ) > Nonlinear control systems

Robust Control for Time-delay Uncertain Systems Based on T-S Fuzzy Model

Author LiBo
Tutor HeXiQin;ZhangDaQing
School Liaoning University of Science and Technology
Course Operational Research and Cybernetics
Keywords T-S fuzzy model delay-dependent non-fragile control free weighting matrices linear matrix inequality
CLC O231.2
Type Master's thesis
Year 2008
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Stability analysis and control of nonlinear time-delay systems are important issues in the control. Based on Takagi-Sugeno (T-S) fuzzy model and LMI method, the thesis focuses on the problems of robust fuzzy control for uncertain nonlinear systems with time-delay, which mainly covers the following three aspects(1) The problem of delay-dependent stability of a class of uncertain T-S fuzzy systems with time-delay is studied. Firstly, free weighting matrices are introduced in the derivative of the Lyapunov function. By employing Lyapunov stability theory, a delay-dependent stability criterion for fuzzy unforced systems is obtained. Then, base on the stability criteria, new sufficient conditions for the existence of fuzzy controller are devised. Because Park or Moon inequality is not employed to relax the inequality in the derivation process, the new criteria is with less conservatism than the exiting ones.(2) The problem of delay-dependent H_∞control for a class of uncertain T-S fuzzysystems with time-delay is studied based on free weighting matrices. Based on freeweighting matrices and Lyapunov stability method, a new delay-dependent robuststability criterion is proposed. The new criterion is less conservative than exiting ones.Based on the stability criterion, sufficient condition for the existence of fuzzy H_∞statefeedback controller is devised in the form of non-linear matrix inequality. Furthermore,by using appropriate parameter setting method and Schur complement, the non-linearmatrix inequality condition is composed into linear matrix inequality condition.(3) The design problem of fuzzy robust non-fragile state feedback controller isdiscussed for a class of uncertain T-S fuzzy systems with time delay. Two classes ofperturbations are considered, namely, additive perturbation and multiplicativeperturbation. Based on free weighting matrices and Lyapunov stability method, sufficientconditions for the existence of fuzzy non-fragile controller are devised and the methods todesign controller inequality are given in terms of LMI.

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