Synthesis of stabilizing control in diffusion systems with Markovian switching

We consider stochastic systems modeled by Ito differential equations with Markovian switching, and propose the parametric description (parametrization) of all static output feedback stabilizing controllers. This controllers provide exponential stability in the mean square of the closed-loop system. Using this parametrization we obtain sufficient conditions of stabilization, which allow to develop an LMI-based algorithm for gain matrixes computation of both static and a dynamic regulators. This algorithm is applied to the solution of a stabilization problem of the inverted pendulum on the moving platform under conditions of step-like mass change and random vibration of the platform.