Robust finite-time contractive stability analysis of faulty linear network-based control systems with an aperiodic sampling and adaptive event-triggered scheme

Abstract

This study investigates the problem of finite-time contractive stability analysis and observer-based ${\mathrm{H}}_{\infty }$ fault-tolerant control (FTC) for linear network-based control systems subject to network-induced time-varying delay. It is assumed that the faults occur in the both actuator and sensor components. For the sake of data transmission reduction, an aperiodic-sampling-based adaptive event-triggered scheme is used, in which the interval between two sampling instants varies within a certain known bound, and the event threshold is adjusted by using the adaptive rule. An unknown input observer (UIO) is used to estimate the system states and faults simultaneously. Then, using Lyapunov–Krasovskii stability theory, delay-dependent sufficient conditions for the observer-based FTC of the networked control system (NCS) are derived. These conditions are presented in the form of linear matrix inequalities (LMIs), ensuring that both the error system and the closed-loop NCS achieve finite-time contractive stability while simultaneously satisfying the ${\mathrm{H}}_{\infty }$ performance index. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design approach.