An algebraic test for asymptotic stability of delay differential systems with commensurate delays

Abstract

An algebraic test for asymptotic stability independent of delay for delay differential systems is presented. The test is developed using the Kronecker product formulation of the frequency dependent Lyapunov equation for delay differential systems. Sufficient conditions for asymptotic stability independent of delay are shown to be equivalent to testing the eigenvalues of a set of constant matrices. Numerical aspects of the algorithms are also discussed.<>