Finite-Time $H_{\infty }$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback

This paper studies the finite-time H_∞ control problem for time-delay nonlinear jump systems via dynamic observer-based state feedback by the fuzzy Lyapunov-Krasovskii functional approach. The Takagi-Sugeno (T-S) fuzzy model is first employed to represent the presented nonlinear Markov jump systems (MJSs) with time delays. Based on the selected Lyapunov-Krasovskii functional, the observer-based state feedback controller is constructed to derive a sufficient condition such that the closed-loop fuzzy MJSs is finite-time bounded and satisfies a prescribed level of H_∞ disturbance attenuation in a finite time interval. Then, in terms of linear matrix inequality (LMIs) techniques, the sufficient condition on the existence of the finite-time H_∞ fuzzy observer-based controller is presented and proved. The controller and observer can be obtained directly by using the existing LMIs optimization techniques. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach.