A canonical decomposition of linear periodic discrete-time systems

Abstract

In this paper a linear periodic discrete-time system is studied. On the basis of simple properties of the subspaces of controllable states and of unreconstructible ones, a canonical structure theorem is derived. This generalizes 1o such a system the classical Kalman decomposition, while preserving the constant dimensionality of the four subsystems which arise when a periodic continuous-time system is decomposed. The dynamic matrices of the non-controllable and/or non-reconstructible subsystems are shown to be non-singular at each time instant, as those for a time-invariant discrete-time system are.