Dynamic self-triggered control for positive fuzzy Markov jump systems with switching transition rates

Abstract

This paper studies the dynamic self-triggered $L_1$-gain control for positive T-S fuzzy Markov jump systems subject to switching transition rates. Bearing in mind the positivity of Markov jump models, a dynamic self-triggered mechanism is crafted based on the 1-norm, wherein the subsequent execution time is precalculated to rely solely on the latest sampled information, thus eliminating the requirement for continual system state monitoring with additional hardware. By utilizing matrix decomposition technique and constructing linear co-positive Lyapunov function, sufficient conditions for the positivity and the exponential stability are derived under average dwell time switching. A detailed analysis of $L_1$-gain performance is conducted. All the mentioned conditions are amenable to being solved through linear programming. Finally, the validity of the obtained results is verified through two examples.