Non-fragile H∞ SMC for Markovian jump systems in a finite-time

Abstract This paper mainly discusses H ∞ finite-time realization for a class of uncertain Markovian jump systems (MJSs) with unmeasurable state via sliding mode control (SMC) method. A key question is how to design an appropriate SMC approach in a finite-time to reduce the effects of model switching and external interference on the overall performance of the system under consideration. First, by designing an appropriate finite-time SMC law based on a non-fragile observer, the state trajectory can reach a specified sliding surface (SSS) within given finite-time interval. Then, by means of time-partitioning strategy, finite-time boundedness (FTBs) criteria including the reaching phase and the sliding motion phase are proposed for uncertain MJSs with H ∞ performance. Second, by solving the corresponding linear matrix inequalities (LMIs), the controller gain and the observer gain are obtained. Finally, a single-link robot arm model (S-LRAM) is given to prove the effectiveness of the proposed method.