Abstract
The existence and uniqueness of the periodic nonnegative solution of the discrete matrix Riccati difference equations with periodic coefficients are discussed.
As is well known, such equations play a central role in the controls as well as filtering theory. The principal result obtained in this paper is that stabilizability and detectability is a necessary and sufficient condition for the existence of a unique nonnegative periodic solution to yield an equilibrium solution and for the associated closed-loop system to be asymptotically stable. This result corresponds to Hewer's result which was discussed with continuous periodic systems.
The proof of sufficiency follows along the line of quasilinearization technique and the necessity is shown by the effective use of the canonical structure theory which is developed to the discrete periodic systems in this paper. Also, for the discrete periodic systems the extended discussions on the definition of stabi-lizability and detectability by Hautas are included.
