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Abstract
A practical stability test for linear retarded delay differential systems is proposed. Based on the fact that all unstable zeros of the characteristic quasipolynomial must lie within a restricted bounded region of the complex plane, the test provides a readily computable necessary and sufficient condition for asymptotic stability. It also copes equally well with both cases of commensurate and non-commensurate delays. Furthermore, a method for evaluating the abscissa of stability of the quasi-polynomial, defined as the largest of the real parts of the zeros of the quasipolynomial, is given. The method is based on a known technique which makes repeated use of a stability test, and thereby avoids the calculation of all the zeros. The stability test and the method for computing the abscissa of stability provide useful computational tools for the design of dynamical systems with delays using the method of inequalities. Numerical examples are given.