Finite-Time Annular Domain Stability and Stabilization of Stochastic Systems With Semi-Markovian Switching

Abstract

In this paper, finite-time annular domain stability and stabilization of Itô stochastic systems with semi-Markovian switching are investigated, where the switching frequency is timevarying, and satisfies a unfixed polytope. A new inequality called reverse differential Gronwall inequality is proposed to address less conservative sufficient conditions for testing the finitetime annular domain stability, and its superiority to modified Gronwall inequality is analyzed. Moreover, sufficient conditions for the existence of state feedback and observer-based finitetime annular domain stabilizing controllers are obtained. In the sequel, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {L}$</tex-math></inline-formula> × <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -mode algorithm is presented for bridging the relationship between the adjustable parameters and the range of transition rates. Finally, an example is provided to illustrate the effectiveness of the proposed methods.