State‐feedback control for almost sure stability of stochastic nonholonomic semi‐Markov jump systems

In this article, we construct a state‐feedback control strategy for the almost sure stability of stochastic nonholonomic semi‐Markov jump systems. This work first introduces semi‐Markov jump dynamics to stochastic nonholonomic systems. The dwell time depends on both the present and subsequent modes, significantly reducing conservatism in dwell time constraints. With the aid of a novel state transformation, the stochastic nonholonomic systems are decoupled. Based on stochastic analysis principles, the backstepping technique, and a multiple Lyapunov‐like function framework, a novel controller is designed, and sufficient conditions are obtained to achieve almost sure stability via the state‐feedback controller. In addition, by adopting the switching strategy, the phenomenon of uncontrollability is eliminated. Finally, an example demonstrates the effectiveness and feasibility of the proposed scheme.