Stochastic stabilizability of a class of discrete-time non-linear systems

Abstract

This paper presents a characterization of all state covariances assignable by a linear static output feedback controller to a class of discrete-time non-linear stochastic systems and a parametrization of all such controllers that will achieve a desired covariance. These results indirectly provide similar results for fixed-order dynamic feedback compensators. This characterization enables one to test the stochastic stabilizability of such systems by output feedback. An alternative formulation of stochastic stabilizability by output feedback is also included. Then, these results are specialized to the state feedback case and presented together with the previous results of the authors' to form a more complete and unified picture of stochastic stabilizability conditions.