A descriptor approach to sliding mode control of systems with time-varying delays

In this note we combine a descriptor approach to stability and control of linear systems with time-varying delays, which is based on the Lyapunov — Krasovskii techniques, with a recent result on sliding mode control of such systems. The systems under consideration have norm-bounded uncertainties and uncertain bounded delays. The solution is given in terms of linear matrix inequalities (LMIs) and improves the previous results, based on other Lyapunov techniques. A numerical example illustrates the advantages of the new method.