Fault-tolerant control and zonotopic interval estimation for discrete-time linear systems based on an event-triggered mechanism

This article investigates the problems of fault-tolerant controller (FC) design and zonotopic interval estimation for a class of discrete-time linear systems subject to unknown-but-bounded (UBB) disturbances and measurement noise. Firstly, a state observer and a fault observer are developed to estimate the system state and the sensor fault based on a designed event-triggered mechanism (ETM). Unlike most existing works, the parameter matrices of the FC and the parameters of the ETM are co-designed, reducing conservatism of parameter design while ensuring system performance. Next, to minimize the influence of unknown disturbances and measurement noise on observation accuracy, the $l_{\infty }$ technique is used to optimize the observer gain. Additionally, using the designed observers, the possible intervals of states and sensor faults are determined through reachability analysis using zonotopes. Finally, a simulation of a well-stirred chemical reactor is performed to validate the effectiveness of the proposed approach.