Robust L1 dynamic output feedback control for a class of networked control systems based on T–S fuzzy model

• The L1L1 norm performance criteria is first provided for nonlinear networked control systems based on T–S fuzzy model.
• Much less conservative results are provided to design the robust L1L1 dynamic output feedback controller for T–S fuzzy networked control systems based on a delay- and basis- dependent Lyapunov–Krasovskii function.
• In consideration with the imperfect networked environment with signal transmission delay and data packet dropout, the systematic design method of the admissible robust L1L1 dynamic output feedback controller is proposed.

This paper investigates the robust L1 dynamic output feedback control problem for a class of nonlinear networked control systems (NCSs) represented by Takagi–Sugeno (T–S) fuzzy model. In consideration with the imperfect networked environment with signal transmission delay and data packet dropout, a fuzzy NCS via dynamic output feedback is established by utilizing the parallel distributed compensation (PDC) technique. The attention is focused on designing the robust L1 controller that guarantees being asymptotically stable of the fuzzy NCS and satisfies a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbance input signals. In particular, we concentrate on constructing a delay- and basis- dependent Lyapunov–Krasovskii function which is in favor of reducing the conservatism, and furthermore, by using the integral inequality method and the Projection Lemma, the peak-to-peak performance criterion is first established. In this way, the design problem of the admissible L1 dynamic output feedback controller can be converted into a convex optimization problem of solving a set of linear matrix inequalities (LMIs). Simulation results are provided to illustrate the effectiveness of the proposed method.