Nonquadratic local stabilization of nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions

Abstract In this paper, the local stabilization problem of continuous-time nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions is investigated using a mode-dependent nonquadratic Lyapunov function. Different from other existing studies, this paper proposes a method that can improve the feasibility of local stabilization conditions (i) by not assuming the maximum allowable bound of the time-derivative of the fuzzy basis functions, and (ii) by utilizing hidden information of the partial derivative of the fuzzy weighting functions with respect to the state variables. Furthermore, since the problem of estimating the attraction region is addressed with consideration of energy-bounded disturbances, the proposed method can be directly applied to the H ∞ control problem without any other assumptions on the magnitude of disturbances.