Zero dynamics of regularly perturbed systems may be singularly perturbed

Abstract

In this paper we present new results on the structure of the zeros of linear and nonlinear systems under perturbation. In particular, we show that when state space descriptions of linear or nonlinear single-input single-output systems with relative degree ≥ 2 are regularly perturbed, then their zero dynamics may be singularly perturbed and show a separation of time scales. In the SISO case, we give asymptotic formulas for the new high frequency zero dynamics arising from the regular perturbation.