Finite-time annular domain stability and stabilization for stochastic semi-Markovian switching systems driven by Wiener and Poisson noises

Abstract

This paper delves into the challenges of finite-time annular domain (FTAD) stability and stabilization for stochastic semi-Markovian switching systems influenced by both Wiener and Poisson noises. Firstly, novel sufficient conditions for assessing FTAD stability are established by leveraging the reverse differential Gronwall inequality (RDGI) and the mode-dependent parameter approach (MDPA). Secondly, state feedback controllers and observer-based controllers are designed, and the improved sufficient stabilization conditions that guarantee the existence of effective controllers are derived. Furthermore, the newly designed algorithms aim to determine the range of transition rates and Poisson jump intensity by meeting the proposed conditions for different adjustable parameters. Finally, we present the numerical examples to substantiate the effectiveness of the proposed methodologies.