Stability criterion for linear commensurate delay systems: A Lyapunov matrix and piecewise constant discretization approach

Abstract

In this work, a new exponential stability criterion of finite dimension based on the delay Lyapunov matrix is derived for linear systems with multiple commensurate delays. It relies on a simple piecewise constant approximation of the matrix kernels of functionals with prescribed derivatives followed by the explicit error bound. The criterion combines an elegant structure of the block matrix, whose positive definiteness is to be tested, with a reasonable matrix dimension.