Improved robust stability criterion for delay systems

This paper develops a novel robust stability criterion with guaranteed performance for a class of linear continuous time-delay systems with polytopic uncertainties. The state-delay is an unknown-but-bounded interval, differentiable time-varying function satisfying some known bounding. The criterion is derived based on the constructive use of a new Lyapunov-Krasovskii functional coupled with integral inequality. The sufficient stability condition is expressed in terms of a linear matrix inequality which manipulates fewer decision variables and requires reduced computational effort. Through a comparison with other existing stability methods, it is established that the developed method retains some useful terms that are frequently ignored and does not use any free-weighting matrices to avoid redundancy. All the developed results are tested on representative examples.