Stochastic stabilization of hybrid differential equations

This paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system. New methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided. These results are then used to examine stochastic stabilization by stochastic feedback controls. Two types of structure controls, namely state feedback and output injection, are discussed. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. A couple of examples and computer simulations are worked out to illustrate our theory.