Finite‐time composite control for fuzzy delayed semi‐Markovian jump systems with multiple disturbances and uncertainty

Abstract

Summary This article is concerned with the issue of finite‐time analysis for fuzzy semi‐Markovian jump systems (S‐MJSs) with multiple disturbances. Takagi–Sugeno fuzzy method is applied to address the nonlinear problem of closed‐loop systems. Unlike the existing research, delay, multiple disturbances, generally uncertain transition rate, uncertain parameters are all analyzed in a unify S‐MJSs framework. The aim of this study is to construct a composite control strategy for stable operation of S‐MJSs with multiple disturbances on the basis of the actual system requirements. For S‐MJSs, conservatism of analysis method and uncertainty of actual system are both the significant problems need to be solved urgently. First, the sufficient condition of S‐MJSs is obtained to guarantee the finite‐time stable performance through mathematical analysis and matrix inequality derivation. Second, disturbance observer based control and H∞$$ {H}_{\infty } $$ control are combined to deal with the effects of multiple disturbances which contain incomplete information disturbance and norm bounded disturbance. Third, fuzzy controller is designed to satisfy close‐loop systems finite‐time performance. Finally, the actual nonlinear example is presented to verify the accuracy of the approach.