Observer-based mode-independent integral sliding mode controller design for phase-type semi-Markov jump singular systems

This paper considers the observer-based integral sliding mode controller design problem of semi-Markovian jumping singular systems with time-varying delays. Firstly, by using a plant transformation and supplementary variable technique in the work of Hou et al, the discussed phase-type semi-Markov jump singular system is equivalently transformed into its associated Markov jump singular system. Secondly, an observer-based sliding mode controller design problem is investigated for the associated singular Markov jump systems. The highlight of this paper is that we construct an observer-based mode-independent integral sliding mode surface function, which is different from the mode-dependant sliding mode surface function in the previous literatures. Based on this, an observer-based sliding mode controller is designed to guarantee that the associated singular Markov jump system meets the reachable condition. Finally, a practical example is presented to demonstrate the efficiency and effectiveness of our obtained results.