Observer-based robust H ∞ control for uncertain Markovian jump systems via fuzzy Lyapunov function

This paper investigates the problem of observer-based robust H ∞ control for a class of continuous-time nonlinear Markovian jump systems (MJSs) with uncertainties, external disturbance and unavailable states that can be represented by Takagi-Sugeno (T-S) fuzzy models. Based on a mode-dependent fuzzy Lyapunov function and by introducing slack matrix variables, a sufficient condition for the existence of the state observer and observer-based robust H ∞ controller for such MJSs are derived by constructing an augmented fuzzy system. Further, by means of congruent transformation in matrix and linear matrix inequality (LMI) method, the results are given in the form of LMIs that can be easily solved by using the convex optimization techniques. Moreover, we also give the result obtained via common stochastic Lyapunov function to compare with the proposed approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.