Annular Finite‐Time Stability and Stabilization in Probability for Nonlinear Stochastic Markov Jump Systems With Impulsive Effects

This article investigates annular finite‐time stability (AFTS) and stabilization in probability for nonlinear stochastic Markov jump systems with impulsive effects. First, a new notion called AFTS in probability is introduced, which is weaker than AFTS in mean‐square sense, and a new proposition that the AFTS in mean square sense implies the AFTS in probability under general assumptions is given by constructing inverse function and Burkholder‐Davis‐Gundy inequality. Second, by the inverse technique of Lyapunov function and dividing the system state at distinct impulsive instants, the testing criterion for AFTS in probability is derived. Moreover, sufficient conditions for state feedback AFT‐stabilizing controller design are obtained, and a set of possible control laws is given in detail. Finally, a numerical example is provided to verify the validity of our proposed results.