Robust stabilization of random-structure systems via switchable static output feedback

A class of jump control systems, whose structure changes in time according to the evolution of a homogeneous Markov chain, is studied. The control system in every fixed mode is described by a linear differential equation. The state vector of the system may also jump when the mode jumps. The number of modes is finite and mode jump process is observable. Necessary and sufficient conditions for the mean-square stabilization of the system via a static output feedback control, which is synchronously switched with mode changes, are formulated. These conditions are generalized to uncertain parameters of mode changes. Sufficient conditions under which a static-feedback control stabilizes the system under uncertainty of control parameters are derived. These results are generalized to the case of dynamic output feedback. Computational aspects of the problem related to the application of linear matrix inequalities are described.