Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions

This paper addresses the state feedback control of nonlinear continuous-time, Markovian-jump systems. The nonlinearity is represented by Takagi–Sugeno fuzzy models and the transition probability matrix is assumed to be partly known: some elements in the matrix are known, some are unknown but with known lower and upper bounds, and some are completely unknown. By making full use of the continuous property of the transition probability matrix, new sufficient conditions for the stochastic stability of the system are obtained in terms of linear matrix inequalities. We show that the conditions given are less conservative than or at least the same as those for existing results. Moreover, using the conditions obtained, we establish a method for design of a H∞ state feedback controller. Numerical examples illustrate the effectiveness of the proposed method.