CYCLOMONOTONICITY AND STABILIZABILITY PROPERTIES OF SOLUTIONS OF THE DIFFERENCE PERIODIC RICCATI EQUATION

This note deals with the Kalman filter associated with a discrete-time linear T-periodic system. The problem considered is that of selecting an initial covariance matrix such that the periodic filter based on the first T values of the Kalman gain is stabilizing. Sufficient conditions are given that hinge on the cyclomonotonicity of the solution of the periodic Riccati equation. Potential applications are found in filter design, quasi-linearization techniques for the periodic Riccati equation, and the design of receding-horizon control strategies for periodic and multirate systems. When specialized to time-invariant systems, our results give rise to new sufficient conditions for the cyclomonotonicity of the solutions of the time-invariant Riccati equation and the existence of periodic stabilizing feedbacks.