The stochastic stability and extended dissipative analysis of semi‐Markov jump systems under dynamic adaptive event‐triggering mechanism

Abstract This paper explores the intersection of stochastic stability and extended dissipative analysis in semi‐Markov jump systems under dynamic adaptive event‐triggering mechanisms, considering nonlinearity and time‐varying delay effects. Although Markov jump systems are widely used in various fields, they suffer limitations due to the exponential distribution of state transition times. To address this, semi‐Markov jump systems have been proposed, accommodating nonexponential distributions and incorporating temporal aspects into state transitions. Four key innovations are presented: a creatively devised dynamic adaptive event‐triggering mechanisms, consideration of time delay and nonlinearity in semi‐Markov jump systems, the adoption of a more simple method to decouple coupling terms, and the use of semi‐Markov jump switching law. Simulation experiments indicate that the achieved theoretical conditions are feasible for realizing extended dissipative and stochastic stability.