Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach

Abstract This paper investigates the finite-time annular domain stability and stabilization of stochastic systems, described by an Ito-type differential equation, in which the systems are driven by both Wiener noises and Poisson jumps. First, a new inequality called reverse differential Gronwall inequality is established to achieve less conservative conditions for finite-time annular domain stability. Second, some sufficient conditions are derived to guarantee that the closed-loop system is finite-time annular domain stable by constructing a state feedback controller and an observer-based controller, respectively. All related conditions can be expressed in terms of matrix inequalities and corresponding algorithms are given. Finally, two numerical examples are presented to verify the validity of the derived results, and the effect of Poisson jump intensity on the boundary of the system states is illustrated.