Finite-Time Adaptive Fault Estimation for Discrete-Time Switched Descriptor Systems

Abstract

This paper proposes a novel finite-time adaptive fault estimation (FE) method for discrete-time switched descriptor systems under mode-dependent persistent dwell-time (MDPDT) switching. Unlike traditional discrete-time FE techniques, which impose restrictive rank conditions on disturbance coefficient matrices, we relax these requirements by decomposing disturbance into virtual perturbation and auxiliary state. Furthermore, we introduce MDPDT switching into the FE framework for switched descriptor systems for the first time, thereby reducing the conservatism inherent in uniform dwell-time approaches. The proposed adaptive observer achieves finite-time estimation of system states, external disturbances, and actuator faults, avoiding the slow and asymptotic convergence typical of existing switched FE schemes. Finally, the effectiveness and superiority of the proposed approach over existing methods are demonstrated through a switched circuit system example. Note to Practitioners—As a special class of hybrid systems, switched descriptor systems offer a unified framework to capture both the dynamic and static behaviors of switched systems, making them well-suited for modeling electronic circuits. In practical applications, faults caused by component wear or abrupt environmental changes are inevitable and can significantly degrade system performance. Therefore, effective fault estimation (FE) methods for switched descriptor systems are crucial to improving circuit system reliability. This work proposes a finite-time adaptive FE approach for discrete-time switched descriptor systems, aiming to achieve faster convergence and enhanced estimation accuracy. A novel decomposition mechanism is employed to separate disturbances into virtual perturbations and auxiliary state variables, thereby relaxing restrictive rank conditions on the perturbation coefficient matrices in the state and output equations. Furthermore, a mode-dependent persistent dwell-time (MDPDT) switching signal is integrated into the FE observer framework, enabling the method to handle both fast and slow switching behaviors within a unified structure. Finally, the effectiveness and superiority of the proposed approach are demonstrated through a representative example involving a switched circuit system.