Hybrid control design for nonlinear chaotic semi-Markov jump systems via fault alarm approach

This paper investigates the stabilisation problem for a class of T-S fuzzy chaotic semi-Markov jump systems against parametric uncertainties, actuator faults and external disturbances. The main objective of this study is to develop a fault alarm-based non-fragile mode-dependent hybrid controller mechanism to withstand the actuator faults in the concerned system, wherein the hybrid control design blends both robust and fault-tolerant control schemes. Therein, the fault-alarm system is configured based on the alarm threshold, which aids in the execution of the hybrid controller. Specifically, it allows the controller to be timely alerted, making it switch from a robust to a fault-tolerant controller, that is, robust control oversees when the system functions without fault and fault-tolerant control takes over when the system encounters a fault. From there on, through the consideration of relevant Lyapunov function, a novel set of mode-dependent sufficient criteria that have a linear matrix inequality structure is acquired, which confirms the $(X,Y,ℨ)$-$\zeta$-dissipativity of the system under study. Following that, the precise design of the robust and fault-tolerant controller is procured by solving the developed sufficient conditions. In the end, the simulation results of Chua’s circuit system are offered to confirm the significance of the theoretical insights acknowledged.