Filtering Design For Uncertain Discrete-time Linear System And Local Control For Continuous-time T-S Fuzzy Model

Robust H2filtering design for uncertainty linear system is an important topic incontrol fields. In recent years, many experts have made important contributions in thisaspect, and design various ways to reduce the conservatism to get better result. Thispaper is concerned with robust H2filtering design for uncertain linear system, in orderto reduce the conservatism further, the iteration algorithm is proposed based on theanalysis of the possible sources of conservatism. Compared with previous works, freematrix variables introduced in the iterative algorithm do not need to satisfy specificstructure, thus，this method can reduce the conservatism. Finally, simulation resultsdemonstrate the effectiveness of the proposed algorithm.Takagi-Sugeno (T-S) fuzzy model is commonly used in the fuzzy controltechnology. In recent years, many researchers have used various methods to study itsstability and stabilization, and achieved fruitful results. For the study of continue T-Sfuzzy model, previous efforts are devoted to the global results. However, for somecontinue T-S fuzzy models, global quadratic stability conditions are not able to achieve.T. M. Guerra solves the analysis of local stability by designing non-quadratic Lyapunovfunction in one of his papers in2009. Based on non-quadratic Lyapunov function,applying the method proposed by T. M. Guerra, the conditions can be expressed asLMIs which solve the problem of stability for continue T-S fuzzy model. Convexoptimization tools are applied to continue T-S fuzzy model in this paper. The Lyapunovfunction level set must be contained in the set C (nonlinear systems can be expressed asT-S model in the set C).It is changed to LMIs to analyze the stability of this kind offuzzy systems and design fuzzy controller such that the corresponding closed-loopsystem is stable and has better performance.Robust filter design is another important topic for Takagi-Sugeno fuzzy. In recentyears, many researchers make contributions in this area, but most of them are fordiscrete system, relatively little for continue T-S model. The robust filter design forcontinue T-S model is discussed in this paper. The problem of differential ofmembership functions is solved by designing non-quadratic Lyapunov function, andsome LMIs are obtained by matrix transformation. Thereby the filter which meets therequirements is designed. Lastly, an example shows the feasibility of this way.