Finite-time annular domain stability and stabilisation of Itô-type stochastic time-varying systems with Wiener and Poisson noises

Abstract

This paper investigates finite time annular domain (FTAD) stability and stabilisation for Itô-type stochastic time-varying systems with continuous Wiener and discontinuous Poisson noises (STVSWPNs). First, using Itô-Levy formula and time-varying multiple quadratic Lyapunov functions, two less conservative FTAD-stability conditions based generalised differential Lyapunov equations (GDLEs) and differential linear matrix inequalities (DLMIs) are obtained. Second, the FTAD stabilisation is studied and some new sufficient conditions for the existence of state feedback and static output feedback controllers are presented by tractable differential linear matrix inequalities. Moreover, a new numerical algorithm is given. Finally, a numerical example and a real-world example are utilised to show the effectiveness of the proposed methods.