Study On Convervativeness Reducing Of Stabilization Condition Of T-S Fuzzy Systems With Time Delay

As an important research field, fuzzy control theory has attracted considerable attention from scientists recently. It has made a great progress in practical control technology. Since time delays are frequently encountered in a variety of engineering systems and are often sources of instability and degradation of control performance in control systems, the study on fuzzy control systems with delays is important in both theory and practice. This dissertation utilizes linear matrix inequality method and integral inequality approach for various stabilization problems of T-S fuzzy systems with time delays to obtain less conservative delay-dependent criteria.To study conservativeness reducing problem of stabilization condition of fuzzy delay system, some integral inequalities are first introduced to analyze the stability criteria of fuzzy systems with constant time delays. The existence condition for guaranteed cost control of the fuzzy systems is obtained, and it is proved theoretically to encompass an established result in the literature as a special case, which shows well the advantages of the integral inequality approach. Moreover, some augmented matrices are introduced into Lyapunov-Krasovskii functional and new integral inequalities are constructed to further reduce conservativeness in the stability for T-S fuzzy systems with time delay. The new method is extended into guaranteed cost problem, and linear matrix inequalities based criterion for obtaining guaranteed cost controller is given. Illustrative examples show that compared with the existing results, the results obtained from the integral inequality method possess less conservativeness, and it also reduces the amount of computation with less matrix variables.For fuzzy systems with interval time-varying delays, improved integral inequalities, constructed for the time-varying issue, are employed to avoid the conservativeness caused by integral area reducing method used in the literature. The delay-dependent stability condition is obtained based on the improved integral inequalities. Moreover, the criteria is extended into the delay-dependent/rate- independent stability condition. Without any integral area reduction, some conservativeness is reduced in the obtained results. Further more, new integral inequalities are constructed for augmented Lyapunov-Krasovskii functional. An illustrative example shows that the methods of this dissertation can lead to much larger upper of delay than the existing results.Robust control for uncertain fuzzy systems with state delay and input delay is investigated. State feedback controller for the fuzzy systems is provided via parallel distributed compensation. A new delay dependent robust stabilization criteria is obtained based on newly constructed Lyapunov-Krasovskii functional and integral inequalities. A method of designing a delay-dependent fuzzy controller based on parameter tuning is described. The numerical example shows the effectiveness of the given method.To reduce the conservativeness exists with common Lyapunov-Krasovskii functional, fuzzy Lyapunov-Krasovskii functional is introduced to consider the delay-dependent H∞control of fuzzy systems with interval time-varying delays. Membership function is introduced into improved integral inqequlities. Since membership function is considered in fuzzy Lyapunov-Krasovskii functional and integral inequalities, some conservativeness is further reduced in stabilization condition of fuzzy delay system. The obtained results encompass the common Lyapunov-Krasovskii functional based results as a special case, which shows well the advantage of the proposed method.The improved integral inequalities are extended into discrete-time case and finite-sum inequalities for quadratic terms are established, the delay- dependent H∞control of fuzzy discrete-time systems with state delays is analyzed. The finite-sum inequalities for quadratic terms are used in combination with memory-less state feedback to derive delay-dependent conditions that guarantee that the resulting closed-loop system has a given H∞performance. Two methods of designing memoryless controller, one based on an iterative algorithm and the other based on parameter tuning, are described.