Abstract: We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.
Abstract: This paper studies the problem of exponential
stability of perturbed discrete linear systems with periodic
coefficients. Assuming that the unperturbed system is exponentially
stable we obtain conditions on the perturbations under which the
perturbed system is exponentially stable.