Robust Stabilization of Markovian Jump Linear Singular Systems with Wiener Process and Generally Incomplete Transition Rates

This paper is devoted to the investigation of robust stability and robust stabilizability for a class of uncertain Markovian jump continuous-time singular systems with Wiener process and generally uncertain transition rates (GUTRs). This new uncertain model is more general than the existing ones and can be applicable to more practical situations because of its uncertain parameters and transition rates. Each transition rate can be completely unknown, or only its estimate value is known. Our interests are focused on establishing sufficient criteria on robust stability and the design of a state feedback controller such that the robust stochastic stability is guaranteed, even if the singular system incorporates GUTRs, Wiener process disturbance and norm-bounded uncertainties. These sufficient criteria are derived in terms of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.