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

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-infinity 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.