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

摘要

This paper studies the finite-time $H_{infty}$ 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 $H_{infty}$ 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 $H_{infty}$ 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.