A relaxed quadratic function negative-determination lemma and its application to time-delay systems

Abstract The quadratic function with respect to the time-varying delay has often been introduced for the analysis of systems with time-varying delays. To determine the negative definiteness of such function, this paper develops a parameter-adjustable-based lemma, which contains the lemma popularly used in literature as a special case and has potential to reduce the conservatism without requiring extra decision variables. A stability criterion for a linear time-delay system is established by using the proposed lemma, whose advantage is demonstrated via a numerical example, and the criterion is finally applied to analyze the stability of load frequency control scheme for a single-area power system.

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