Basis-dependent and delay-dependent results on robust L1 filtering for networked control systems

Abstract

Persistent and amplitude-bounded disturbances are nowadays considered for various engineering applications. Whereas the traditional H∞ and L2–L∞ filtering methods under the energy-bounded external disturbances assumption cannot receive good noise suppression effect. To effectively reflect the capability of disturbances suppression, this paper proposes a robust L1 filtering approach for a class of nonlinear networked control systems (NNCSs) described by Takagi–Sugeno (T–S) fuzzy model. According to the analysis of the typical time-delay issue induced by communication network and the parallel distributed compensation (PDC) technique, a fuzzy filtering error system is established. Attention is focused on designing the robust L1 filter that guarantees the fuzzy filtering error system to be asymptotically stable and to have a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbances. In particular, we concentrate on the delay-dependent case, using a basis-dependent Lyapunov–Krasovskii functional which refers to reducing the conservatism, the peak-to-peak performance criterion is first proposed. The integral inequality method and linear matrix inequality (LMI) technique are adopted during the process of robust L1 stability analysis. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed method.