Stochastic stability and stabilization of a class of state-dependent jump linear systems

TL;DR

This paper analyzes the stochastic stability and stabilization of state-dependent jump linear systems, providing numerically solvable conditions using linear matrix inequalities and illustrating results with numerical examples.

Contribution

It introduces a framework for stability and stabilization analysis of state-dependent jump linear systems with conditions expressed as linear matrix inequalities.

Findings

Established sufficient conditions for stochastic stability.

Provided stabilization criteria for the system.

Validated results through numerical examples.

Abstract

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state variable, and addressed the problem of stochastic stability and stabilization analysis for the proposed system. Numerically solvable sufficient conditions for the stochastic stability and stabilization of the proposed system is established in terms of linear matrix inequalities. The obtained results are illustrated in numerical examples.