Output Reversibility in Linear Discrete-Time Dynamical Systems

Abstract

Output reversibility involves dynamical systems where for every initial condition and the corresponding output there exists another initial condition such that the output generated by this initial condition is a time-reversed image of the original output with the time running forward. Through a series of necessary and sufficient conditions, we characterize output reversibility in linear single-output discrete-time dynamical systems in terms of the geometric symmetry of its eigenvalue set with respect to the unit circle in the complex plane. Furthermore, we establish that output reversibility of a linear continuous-time system implies output reversibility of its discretization regardless of the sampling rate. Finally, we present a numerical example involving a discretization of a Hamiltonian system that exhibits output reversibility.