Takagi–Sugeno Model-Based Sliding Mode Observer Design for Finite-Time Synthesis of Semi-Markovian Jump Systems

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.