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

In this article, finite-time annular domain stability and stabilization of Itô stochastic systems with semi-Markovian switching are investigated, where the switching frequency is time-varying, and satisfies a unfixed polytope. A new inequality called reverse differential Gronwall inequality is proposed to address less conservative sufficient conditions for testing the finite-time annular domain stability, and its superiority to modified Gronwall inequality is analyzed. Moreover, sufficient conditions for the existence of state feedback and observer-based finite-time annular domain stabilizing controllers are obtained. In the sequel, a
$\mathscr {L}$
×
$N$
-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.