New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays

This paper deals with the problem of delay-dependent robust stability for linear systems with time-varying structured uncertainties and multiple time-varying state delays. Based on Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, some new delay-dependent stability criteria in terms of LMIs are derived by taking the relationship between the terms in the Leibniz–Newton formula into account. Since free weighting matrices are used to express this relationship and appropriate ones are selected by means of LMIs, the new improved criteria are much less conservative and more general. Numerical examples and simulation suggest that the results are effective and are an improvement over previous ones.