Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique

This paper investigates the problem of sensor fault estimation and fault-tolerant control for Markovian jump systems with time delay and Lipschitz nonlinearities. The issues involved here are: i) sensor faults; ii) model Lipchitz nonlinearities; iii) system structure changes governed by Markovian jumping parameters; and iv) time delay in system states. Such type of mathematical models can represent a large number of practical systems in the actual engineering. A new estimation technique (named proportional and derivative sliding mode observer) is developed to deal with this design problem. The proposed observer is mode-dependent type in which a derivative gain and a proportional gain are introduced to provide more design freedom, and a discontinuous input term is introduced to eliminate the effects of sensor faults. By employing the developed estimation technique, the asymptotic estimations of system states and sensor faults can be obtained simultaneously. Based on the estimation, an observer-based fault-tolerant control scheme is developed to stabilize the resulting closed-loop system. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique.