Regional Pole Assignment Based On T-S Model

Due to the D-stability can satisfy the design requirements, there are many researches onD-stability, for example, robust D-stability, D-stability for descriptor system, D-stability offuzzy system. Moreover, the D-stability can not only satisfy the stability but also can get goodtransient response. D-stability is a effective way for pole placement to reduce conservation.Compared with common Lyapunov function, fuzzy Lyapunov function can get less conservationin the stability analysis and controller design.This paper concentrates on the D-stability of fuzzy system, fuzzy descriptor system andlinear time-invariant system with state-derivative feedback. The D-stability condition of closed-loop system is discussed at the same time.First, the paper studies the controller design problem for a class of fuzzy systems withconstraints on the pole location. The fuzzy system is described by the T-S fuzzy model anda fuzzy Lyapnov function is proposed to obtain a less conservative controller design method,which could be solved by a set of linear matrix inequalities. Numerical examples illustrate theeffectiveness of the proposed approach.Next, the paper investigates the pole placement problem for a class of fuzzy descriptorsystem. Firstly, based on fuzzy Lyapunov function approach and with the introduction of somefree matrices, new sufficient conditions for the stability of fuzzy descriptor system with polesconstraints are presented. Then we design fuzzy controller for the fuzzy descriptor control sys-tems which guarantees the poles of the closed-loop system to lie in some given LMI region. Allthe conditions are formulated in terms of linear matrix inequality approach. At last, Numericalexamples are given to illustrate the efficiency of the proposed approach.Finally, the paper discusses the pole placement of T-S fuzzy system with state-derivativefeedback. Based on the sufficient robust D-stability condition for the linear time-invariant sys-tem with norm bounded uncertainty, a new sufficient D-stability condition for T-S fuzzy systemwith state-derivative feedback is presented. By introducing some free matrices and fuzzy Lya-punov, all the proposed result has low conservation. In addition, the result condition is convertedto LMI. Numerical examples illustrate the effectiveness of the proposed approach.