Stochastic stability and stabilization of state-dependent jump linear system

This paper deals with a continuous-time state-dependent jump linear 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 analysis and control synthesis for the proposed system. Numerically solvable sufficient conditions for the stochastic stability of the proposed system are established in terms of linear matrix inequalities. The state feedback controller is accordingly developed. The obtained results are illustrated in numerical examples.