Robust state-feedback stabilization of jump linear systems via LMIs

We consider a linear system subject to Markovian jumps, with a time-varying, unknown-but-bounded transition probability matrix. We derive LMI conditions ensuring various second-moment stability properties for the system. The approach is then used to generate mode-dependent state-feedback control laws which stabilize the system in the mean-square sense. When the transition probability matrix is constant and known, our conditions are necessary and sufficient.