Sampled‐data reliable control for T–S fuzzy semi‐Markovian jump system and its application to single‐link robot arm model

This study investigates the sampled‐data reliable control for a class of Takagi‐Sugeno (T‐S) fuzzy semi‐Markovian jump system (FSMJS). The system under consideration involves semi‐Markov stochastic process that is described by the property of cumulative distribution function. To relax the difficulty of finding upper bounds in sample‐and‐hold behaviour of the FSMJS, a novel method named mismatched membership function is presented. Sufficient conditions that can guarantee the T–S FSMJS to be stochastically stable are given. More precisely, the reliable sampled‐data controller is designed in terms of linear matrix inequalities. Finally, the validity of the presented approach is demonstrated by a controller design for a single‐link robot arm model.