Abstract
There are a number of recent results aimed at developing finite necessary and sufficient stability tests for linear time-invariant time delay systems within the framework of Lyapunov-Krasovskii functionals with prescribed derivative approach. These tests are based on the concept of Lyapunov matrix. They usually require verification of positive definiteness of a certain block matrix whose blocks correspond to the Lyapunov matrix evaluated at several discretization points. In this work, we present a new test of this kind which employs a combination of the discretized Lyapunov functionals method of K. Gu and the functionals with prescribed derivative approach. Unlike existing combinations of those techniques, we avoid discretization of the functional's derivative and use the methodology of the necessary and sufficient stability tests development instead. We show a connection between our test and some of the existing results.
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