LMI Robust Stability Condition for Linear Systems with Time-Varying Elemental Uncertainties, Norm-Bounded Uncertainties and Delay Perturbations

Abstract

The stability robustness of linear dynamic systems with time-varying elemental uncertainties, norm-bounded uncertainties and delay perturbations is investigated. A sufficient condition in terms of linear matrix inequalities (LMIs) is proposed to ensure that the linear systems with time-varying elemental uncertainties, norm-bounded uncertainties and state-delay perturbations is asymptotically stable. Two examples are given to illustrate the use of the proposed LMI sufficient condition. To see the merit of the proposed condition, Example 1 discusses the case of only both time-varying elemental and norm-bounded uncertainties, for comparison to an existing one reported recently. It shows that the proposed LMI sufficient condition is less conservative than the existing criterion.