Robust Non-fragile H_∞ Fuzzy Control for Uncertain Nonlinear-Delayed Hyperbolic PDE Systems

In this paper, we consider the robust non-fragile H_∞ fuzzy control for uncertain nonlinear delayed hyperbolic partial differential equation (PDE) systems, which can represent the dynamics of most industrial processes, such as plug-flow reactors, fixed-bed reactors, tubular heat exchangers, traffic flows, and wave equations. Initially, a Takagi–Sugeno (T–S) fuzzy-delayed hyperbolic PDE model is presented to describe the uncertain nonlinear delayed hyperbolic PDE system. Subsequently, based on the T–S fuzzy delayed hyperbolic PDE model, spatial linear matrix inequality (SLMI) based sufficient conditions to ensure exponential stability with an H_∞ performance are obtained via utilizing the Lyapunov direct method. Then, to solve the SLMIs, the robust non-fragile H_∞ fuzzy control problem for uncertain nonlinear delayed hyperbolic PDE systems is formulated as an LMI feasibility problem. Finally, two examples on a Lotka–Volterra PDE system and a non-isothermal plug-flow reactor (PFR) are presented to illustrate the effectiveness of the presented control method.