Robust stabilisation of uncertain time-delay systems containing saturating actuators

The delay-dependent memoryless robust stabilisation problem for a class of uncertain linear systems containing multiple time-delays and a saturating actuator is considered. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and multiple time-delays in both state and control; the delays are assumed to be constant bounded but unknown. A new sufficient condition for the existence of a memoryless robust stabilising control law is derived based on the Lyapunov theorem and linear matrix inequality approach. The results depend on the size of delays and are given in terms of several linear matrix inequalities. A numerical example is presented to illustrate the results obtained