Output Feedback Stabilizing Control and Passification of Switching Diffusion Systems

A parametric description of static output feedback stabililizing controllers for diffusion systems with Markovian switching is presented. This description is expressed in terms of coupled linear matrix equations and non-convex quadratic matrix inequalities which depend on parameter matrices similar to weight matrices in LQR theory. A convexifying approximation technique is proposed to obtain the LMI-based algorithms for computing of the gain matrix. These are non-iterative and used computationally efficient SDP solvers.The results are then applied to simultaneous stabilization of a set of diffusion systems, robust stabilization and stochastic passification problems. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed method.