Robust \(H_{\infty}\) fuzzy control for nonlinear discrete-time stochastic systems with Markovian jump and parametric uncertainties (Q1717907)

Summary: The paper mainly investigates the \(H_{\infty}\) fuzzy control problem for a class of nonlinear discrete-time stochastic systems with Markovian jump and parametric uncertainties. The class of systems is modeled by a state space Takagi-Sugeno (T-S) fuzzy model that has linear nominal parts and norm-bounded parameter uncertainties in the state and output equations. An \(H_{\infty}\) control design method is developed by using the Lyapunov function. The decoupling technique makes the Lyapunov matrices and the system matrices separated, which makes the control design feasible. Then, some strict linear matrix inequalities are derived on robust \(H_{\infty}\) norm conditions in which both robust stability and \(H_{\infty}\) performance are required to be achieved. Finally, a computer-simulated truck-trailer example is given to verify the feasibility and effectiveness of the proposed design method.