Zeros and zero dynamics of switching systems

A notion of zero dynamics for switching linear systems is introduced by using a structural geometric approach. The zero dynamics for a switching system is shown to be represented by a family of dynamics that characterize the way in which the stability of each mode is affected when the overall system is made maximally unobservable by means of a state feedback. The comparison between the elements of the zero dynamics of a switching system and the classical zero dynamics of each mode shows differences that are due to the dynamics generated by the switching and by the interaction between the modes. The role of the zero dynamics in characterizing the stability of the compensated system is similar to that found in the classical linear case, although the results in the switching framework are weaker. Copyright (c) 2023 The Authors.