Input Redundancy of Switched Systems Concerning the Switching Signal

In this paper, we investigate the concept of input redundancy of switched systems, where the switching signal is the control input. An input redundant system in this context describes a system in which the same output trajectory can be generated by non-equivalent switching signals. The concept of equivalence in switching signals means that two signals generate identical state trajectories under identical initial conditions. Unlike the linear time-invariant case where input redundancy is uniform in the initial condition, this property is absent in the considered study. For autonomous switched linear systems, we developed a strategy to verify the existence of initial conditions where non-equivalent switching signals produce the same output. A numerical example is presented to illustrate the proposed strategy, for which we also compute the entire set of initial conditions that lead to input redundancy.