Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions

Abstract

Abstract Representation of solutions of delayed differential equations with multiple delays and periodic coefficients is established. Consequently, results on stabilizability of weakly delayed closed-loop systems and stability of non-weakly delayed periodic systems are proved. The stabilizability result is an extension of the classical Brunovský theorem for linear periodic systems of ordinary differential equations to a class of delay differential equations with pairwise permutable matrix functions.