Stability Analysis And Reliable Control For Switched Fuzzy Systems

As a kind of important new type of complex system, switched fuzzy system has thewidespread application prospect and theoretical research value, which combines thecharacteristics of the switched systems and the characteristics of fuzzy systems. Thecontrol of system is more accurate and flexible by the interaction of continuous dynamicsand discrete dynamic. At the same time, the possibility of the fails for system internalcomponents is increased because of the production process becomes more complex withthe development of industry, and the difficulty of study for the system reliable controlproblem is exacerbated. Compared with the results of switched systems and fuzzy systems,the study results of switched fuzzy systems are very few, and many problems need to beresearched. For the case of actuator with “serious failure”, in which case the unfailed actuatorscan not stabilize the given original system under the traditional control method, this stabilityand reliable control problem of classes of switched fuzzy system is considered to guaranteethat the unfailed actuators can stabilize the switched fuzzy system by switching technology inthis paper. The main contributions are as follows.Firstly, the stability problem for a class of switched fuzzy systems with stateuncertainty and control uncertainty is studied. Arbitrary switching law and designswitching law are considered respectively. The state feedback reliable controller is built byusing single Lyapunov function method. The stability conditions are obtained in terms ofLMIs. A simulation example shows the effectiveness of the conclusion.Secondly, non-fragile reliable control problem is researched for a class of switchedfuzzy system. By using single Lyapunov function method, the sufficient conditions areobtained, which to ensure non-fragile reliable controllers are existed in form of LMIs. Asimulation example illustrates the effectiveness of the reliable controller design process andalgorithm. Next, the reliable control of a class of switched fuzzy time-delay system is studied, inwhich time-delay are constants. For switched fuzzy systems with state time-delay andswitched fuzzy systems which contain state time-delay simultaneous with import time-delay, the state feedback reliable controllers are built via using multiple Lyapunov functionmethod. The asymptotic stability conditions are obtained based on LMIs. A simulationresults verify the effectiveness of the proposed method.Then, the reliable control of a class of switched fuzzy systems with time-varyingdelay is studied. The designing scheme of the state feedback reliable controllers is given.The sufficient conditions of delay-dependent are given in a set of LMIs. And simulationexample is given.Finally, the work content of this paper is summarized and the further study problemsare point out.