Self-Triggered State-Feedback Control for Stochastic Nonlinear Systems With Markovian Switching

Abstract

This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically $ {p}$ -moment exponential stability with respect to an additional disturbance and the practically $ {p}$ -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Ito’s formula, Fubini’s theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen’s inequality technique, properties of $ {\mathcal {K}}$ -function and result on $ {p}$ -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature.