Algebraic Solution of Riccati Equations in Discrete, Periodically Time-Varying System with Detectability and Stabilizability
Toshimitsu Nishimura, Hiroyuki Kano · Transactions of the Society of Instrument and Control Engineers · 1978
The matrix Riccati equation with coefficients varying periodically with time is discussed for discrete systems in this paper. The solution of such equation plays an important role in the application of control and estimation theory. The necessary and sufficient condition for the existence of a unique, non-negative definite and periodic solution as well as the asymptotical stability of the associated closed-loop system is derived and it is related to the stabilizability and detectability of the discrete system.