Control Synthesis And Filter Design For Affine Fuzzy Systems Via Linear Matrix Inequalities

With the developments of the science, we have more requirements for control systems and the control systems are more complex. The controlled object or process often is nonlinear, subject to some random disturbances and uncertainties, so that its mathematical model, which can satisfy our demands, is not available. For the control system, the conventional control theory is not applicable. However, the fuzzy control techniques with a property of human language can overcome the difficulties. In particular, stability analysis and control synthesis of nonlinear systems described by T-S fuzzy models appeal many researchers’interest and many important progresses have been achieved. Due to the inherent nonlinearities of T-S fuzzy systems, it is still a very important task to exploit more effective conditions for stability analysis and control synthesis. Furthermore, since the state variables in control systems are not always available, state estimation is also a significant and chanllenge problem.Based on the previous works of other researchers, this thesis further studies some control problems of T-S fuzzy systems, which are given as follows:compared with the research for the homogeneous T-S fuzzy systems, we consider the affine T-S fuzzy systems, which is more general. A novel linear matrix inequlity technique is proposed firstly, by introducing some extra slack variables, a stabilizing condition under which the affine system is quadratically stabilizable is derived and which leads to less conservative LMI characterizations. Furthermore, we investigate the problem of robust H∞filtering for affine fuzzy systems. A novel fuzzy modeling method is proposed, and a fuzzy-basis-dependent H∞filter design method is obtained by using a piecewise Lyapunov function. Compared with the existing results, the proposed filter design method leads to less computation burden.The considered main issues are given as follows:In Chapter1, the background and the development of fuzzy control are summarized and analyzed.In Chapter2, some preliminaries, definitions and lemmas which will be used later are presented.In Chapter3, the state feedback control synthesis problem for a class of continuous affine fuzzy systems is discussed. First, based on the membership function, we partition the state space into some regions, and design the corresponding controllers. The new designed membership functions can guareteen the amooth transition among these controllers. Finally, a novel control synthesis condition is derived in the formulation of linear matrix inequalities (LMIs).In Chapter4, the problem of state feedback controller design for a class of nonlinear systems is studied, which is expected to have less conservatism. First, a new decouple technique is proposed to decouple the system matrix and the Lyapunov matrix. The obtained result can cover the existing results in theory. Then a new stablity analysis condition is presented and the corresponding controller synthesis method is obtained in the formulation of LMIs. Furthermore, an extended H∞performance analysis of a class of affine fuzzy systems is presented, and the H∞controller synthesis condition is derived.In Chapter5, the problem of robust H∞filtering for descret affine T-S fuzzy systems is investigated. The system outputs have been chosen as the premise variables. By introducing the S-procedure and adding some slack matrix variables, a fuzzy-basis-dependent H∞filter design method is obtained in the formulation of LMIs. Compared with the existing results, the proposed method leads to less computation burden.In Chapter6, the results of the dissertation are summarized and further research topics are pointed out.