Stability, $l_2$ -Gain Analysis, and Parity Space-Based Fault Detection for Discrete-Time Switched Systems Under Dwell-Time Switching

This paper studies the fault detection problem for a class of discrete-time switched linear systems under dwell-time (DT) constraints, using the parity space-based approach. The DT-dependent Lyapunov function is employed to investigate the asymptotic stability with less conservatism and to solve the constant l
₂
-gain performance analysis problem, and its advantage is verified compared to the time-independent Lyapunov function approach. The corresponding switching residual generation is made to carry out the desired fault detection in the framework of parity space-based model. Then, by means of solving a generalized eigenvalue-eigenvector problem, the parity space matrices design is implemented. A quantitative relationship is established between the optimization performance and the choice of the parity space order. Two numerical examples are utilized to demonstrate effectiveness of the developed fault detection approach, including an application to switched RLC circuits.