Robust stability of linear periodic systems

A new method for analyzing the robust stability of linear periodic systems is proposed, which is based on the ideas of commutator calculus in combination with Lyapunov’s direct method. The stability analysis of a linear nonautonomous system of ordinary differential equations is reduced to the stability analysis of a linear system of differential equations with impulse action, for which Lyapunov’s direct method is used. New sufficient conditions for the robust stability of a linear periodic system with non-periodic perturbations are established. Some illustrative examples on the robust stability analysis of linear systems are given.