Robust normalisation and P–D state feedback control for uncertain singular Markovian jump systems with time‐varying delays

Abstract

This study is concerned with the problem of robust normalisation and stabilisation of singular Markovian jump systems (SMJSs) with time-varying delays and parameter uncertainties. The main aim is to design a proportional and derivative state feedback controller to realise the normalisation and stabilisation of the delayed SMJSs. Based on the constructed Lyapunov–Krasovskii functional, sufficient conditions are presented in terms of linear matrix inequalities via utilising the free-weighting matrix method. Illustrative examples including an resistor inductor capacitor (RLC) circuit network are employed to demonstrate the effectiveness and usefulness of the obtained results.