INVARIANT-MANIFOLDS AND PROJECTIVE COMBINATIONS OF SOLUTIONS OF THE RICCATI DIFFERENTIAL-EQUATION

In this paper, we show how families of solutions of the general Riccat i differential equation (RDE) can be generated via projective combinat ions of a given number of reference solutions. Our approach is based u pon the extension of the domain of the equation to the Grassmannian ma nifold and the application of the Radon Lemma. In this context, we bri efly discuss the relevance of our results to the study of the invarian t manifolds of the equation and compare them to existing results conce rning representation formulas for solutions of (RDE). The results of t he paper have been motivated by the recent characterization of solutio ns of the (RDE) given. in M. Pavon, D. D'Alessandro, Families of solut ion of matrix Riccati differential equations, SIAM J. Control Optim., 35 (1) (1997) 194-204, which extends the classical results on the alge braic Riccati equation due to Willems, Coppel and Shayman. (C) 1998 El sevier Science Inc. All rights reserved.