Fault detection and isolation for discrete-time Markovian jump systems with generally bounded transition probabilities: A zonotope-based method

This paper addresses the fault detection and isolation for a class of discrete-time Markovian jump system with generally bounded transition probabilities. The proposed method is mainly based on a bank of [Formula: see text] robust observers, which can detect the actuator fault occurrence and, even more, can locate those subjected to the fault. Furthermore, the performance and the robustness of the designed [Formula: see text] robust observer are disseminated respect to disturbances and measurement noises. In particular, we propose the zonotop-based dynamic threshold to predict the ranges of the residual, which shows less conservatism in comparison to traditional methods. Finally, pertinent simulations are performed to corroborate the potential and superiority of the proposed method. In general, the proposed method offers effective fault detection and isolation scheme for Markovian jump systems, which can detect the fault timely and accurately with lowering the rate of fault missing report to a great extent, thus having practical value.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.