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

Abstract

This paper studies finite‐time annular domain stability (FTADS) and stabilization for stochastic Markovian switching systems driven by both Wiener and Poisson noises. Firstly, new sufficient conditions, based on the common parameter approach (CPA)/mode‐dependent parameter approach (MDPA), are presented to make the stochastic Markovian switching systems FTADS. Secondly, the finite‐time annular domain stabilization (FTAD‐stabilization) is discussed. The state feedback controller (SFC) and the dynamic output feedback controller (DOFC) are designed by CPA/MDPA, respectively, and some new sufficient conditions are given for the existence of these controllers. Moreover, an algorithm is presented to find the value ranges of some parameters, which shows the superiority of MDPA. Finally, a numerical example is supplied to verify the validity of our results.

Event‐triggered annular finite‐time H∞$$ {H}_{\infty } $$ filtering for discrete‐time mean‐field stochastic systems

“…The corresponding AFTB criterion of the FES is derived in Theorem 1. Different from References 25,40, and 38, the LK in this article is constructed by two parts, $$$ \overline{x}(t)-\mathcal{E}\overline{x}(t) $$$ and $$$ \mathcal{E}\overline{x}(t) $$$. Once $$$ \mathcal{E}\overline{x}(t)=0 $$$, $$$ \mathcal{E}\overline{v}(t)=0 $$$ and $$$ \omega (t)=0 $$$ in FES (7), Theorem 1 can be regarded as a parallel development for discrete‐time case of Theorem 1 in Reference 28 with one mode and $$$ d(t)=0 $$$.…”

Observer-based Finite-time Boundedness of Itô Stochastic Markov Jump Systems with Time-varying Delay

“…(15) Taking mathematical expectation of the whole of (15), and then integrating it from 0 to 𝑡, one has…”

“…The analysis of output feedback control is extremely significant in order to avoid measuring the system state and to reduce external disturbances. For example, sufficient conditions for finite-time stabilization of 𝐼𝑡𝑜 ̂ stochastic systems with Markov switching under the action of two controllers were given in [15]. Yan et al designed state feedback controller and OBC through a mode-dependent approach, and gave a number of conditions for the existence of these with less conservativeness in [16].…”

Finite-Time Annular Domain Stability and Stabilization of Regime-Switching Jump Diffusion System

“…There are many papers about finite-time annular domain stability and the systems in most of the papers involves only one of Markov chain and Poisson jump [1], [2], [5]. There are a few papers containing Markov chain and Poisson jump [3], [18]. All of them use the Lyapunov exponent and linear matrix inequality to give the sufficient condition for finite-time annular domain stability of stochastic systems [1]- [3], [5], [18].…”