NORMALIZED COPRIME FACTORIZATIONS FOR LINEAR TIME-VARYING SYSTEMS

In this paper we show that a finite dimensional linear time-varying continuous-time system admits normalized coprime factorizations if and only if it admits a stabilizable and detectable realization. We construct state-space formulas for these factorizations using the stabilizing solutions to standard Riccati differential equations. In the process. we give a simple proof that stabilizability and detectability are sufficient to ensure the existence of such solutions. Based on these results. and on recent advances in the theory of H(infinity) optimization. we present an algorithm to compute the distance between two systems in the gap metric.