Controller Design And Application For Fuzzy Bilinear Systems

In the study of controlling method for complex nonlinear system, T-S fuzzy model is utilized to approximate the controlled plant thus for system analysis and controller design. However, the local systems which comprise the T-S fuzzy model tend to be linear, as the research object becomes more and more complex, the traditional linearized models can't meet the existing control objectives and describe some special nonlinear systems under some circumstance. Hence, the study of fuzzy bilinear system is very important and can process real significance. This paper is based on the concept of T-S fuzzy control, combining with the Lyapunov functional approaches, employing parallel distributed compensation (PDC) scheme and linear matrix inequalities (LMIs) technique, the nonlinear systems described by the T-S fuzzy bilinear model is studied. This main topic of dissertation includes the followings:1) The reviewed basic theory. An introduction to the course of development and research status of T-S fuzzy bilinear system control including background of this study is presented; a short description of T-S fuzzy model, how to transform a nonlinear system into a controlled bilinear one, pole allocation theorem, linear matrix inequalities as well as some common lemmas are showed.2) For a class of continuous-time fuzzy bilinear systems with norm-bounded and parametric uncertainties, the problem of controller design with amplitude limited is studied. Combined with Lyapunov stability theory, the existence conditions of the constrained controller for the closed-loop system are given by using linear matrix inequalities, then, introduce the improved cone complementarity linearization methods, a new approach to constrained controller design for fuzzy bilinear systems is presented.3) The problem of T-S fuzzy bilinear systems with belt-shaped regional pole constraints is presented. Based on the T-S fuzzy bilinear method, combined with the system stability analysis theory and quadratic performance index, the poles of the closed-loop system is allocated in a narrower band to ensure the good steady performance and dynamic performance for the fuzzy closed-loop system.4) For a class of nonlinear systems with Markovian jumping parameters which transfer probabilities is kown, the T-S fuzzy bilinear model is utilized to approximate the real nonlinear character. Lyapunov stability theory is employed to analyse the stabilities of the system, the design method of controllers which depend on the jumping mode is given by using linear matrix inequalities, thus keep the random stable for the jumping systems.