H∞ fault-tolerant fuzzy intermittent control for nonlinear hyperbolic PDE systems with multiple delays and actuator failures

Abstract

This study presents an $H_{\infty }$ fault-tolerant fuzzy intermittent control approach for the nonlinear hyperbolic partial differential equation (PDE) systems with multiple delays and actuator failures (MDAFs). Firstly, the nonlinear hyperbolic PDE systems with MDAFs are characterized by the Takagi–Sugeno (T–S) fuzzy delayed hyperbolic PDE model. Next, by employing the Lyapunov direct method, this paper demonstrates the robust exponential stability using spatial linear matrix inequalities (SLMIs) based on a new switching Lyapunov functional (LF). Furthermore, the $H_{\infty }$ fault-tolerant fuzzy intermittent control issue for nonlinear hyperbolic PDE systems with MDAFs is transformed into the LMI feasibility problem to deal with the SLMIs. Lastly, the feasibility of the constructed control strategy is demonstrated by two illustrative examples.