Mixed H₂/H_∞ Fault-Tolerant Sampled-Data Fuzzy Control for Nonlinear Parabolic PDE Systems Under Deception Attacks

This paper addresses mixed H₂/H_∞ fault-tolerant sampled-data (SD) fuzzy control for nonlinear space-varying parabolic partial differential equation (PDE) system under deception attacks. Firstly, a T–S fuzzy PDE model is given to exactly describe the nonlinear space-varying parabolic PDE system. Secondly, a fault-tolerant SD fuzzy controller via the spatial linear matrix inequalities (SLMIs) is developed based on a Lyapunov functional which is continuous at sampling times but not necessary to be positive definite in sampling intervals such that the closed-loop PDE system is exponentially stable with a mixed H₂/H_∞ performance. Then, to solve the SLMIs, the fault-tolerant SD fuzzy control problem for space-varying parabolic PDE system is formulated as linear matrix inequality feasibility problem. Furthermore, the design condition of the suboptimal mixed H₂/H_∞ fault-tolerant SD controller subject to deception attacks can be derived by considering the property of membership functions. Lastly, two examples are given to illustrate the design method.