Descriptor state‐bounding observer design for positive Markov jump linear systems with sensor faults: Simultaneous state and faults estimation

Abstract

This article presents a descriptor observer design approach for positive Markov jump linear systems subject to interval parameter uncertainties and sensor faults. First, by taking the sensor fault term as an auxiliary state, an augmented descriptor system is constructed. A pair of positive observers with state-bounding feature is then proposed, which enables simultaneous estimation of the system state and sensor faults. A necessary and sufficient condition on existence of the desired state-bounding observer is derived by considering positivity and robust mean exponential stability of corresponding observer error dynamics. An iterative optimization algorithm is developed for the computation of the optimized observer matrices. Finally, a numerical example is presented to show the validity of the proposed methods.