State feedback control for stochastic Markovian jump delay systems based on LaSalle-type theorem

This paper investigates the problem of stochastic stability and stabilization of stochastic Markovian jump delay systems (SMJDSs) based on LaSalle theorem. The time delays are assumed to be time-varying and numerous stochastic disturbances are considered. Attention is focused on the design of the mode-dependent state feedback controller for SMJDSs based on LaSalle theorem such that the closed-loop SMJDSs are almost surely asymptotically stable. The sufficient conditions for the solvability of the state feedback control problem are obtained in terms of linear matrix inequalities (LMIs). When the LMIs are feasible, the desired state feedback controller is also given. Two numerical examples including the vertical take-off and landing (VTOL) helicopter system are employed to demonstrate the effectiveness and usefulness of the method proposed in this paper