Sliding‐mode‐based admissible consensus of nonlinear singular stochastic uncertain semi‐Markov multi‐agent systems with time‐varying delay

Abstract

Abstract In this paper, the sliding mode control of nonlinear singular stochastic uncertain semi‐Markov multi‐agent systems with time‐varying delay are studied. Firstly, a new integral sliding surface function is designed. Secondly, a new sufficient condition in the form of linear matrix inequality is derived to guarantee the stochastic admissibility by using the semi‐Markov–Lyapunov function. Thirdly, a sliding mode control law can be synthesised to ensure the reachability of the predefined sliding surface. Finally, an example is given to demonstrate the effectiveness of the result.