CONVERGENCE OF THE TIME-INVARIANT RICCATI DIFFERENTIAL-EQUATION AND LQ-PROBLEM - MECHANISMS OF ATTRACTION

The nature of the attraction of the solution of the time-invariant mat rix Riccati differential equation towards the stabilizing solution of the algebraic Riccati equation is studied. This is done on an explicit formula for the solution when the system is stabilizable and the hami ltonian matrix has no eigenvalues on the imaginary axis. Various aspec ts of this convergence are analysed by displaying explicit mechanisms of attraction, and connections are made with the literature. The analy sis ultimately shows the exponential nature of the convergence of the solution of the Riccati differential equation and of the related finit e horizon LQ-optimal state and control trajectories as the horizon rec edes. Computable characteristics are given which can be used to estima te the quality of approximating the solution of a large finite-horizon LQ problem by the solution of an infinite-horizon LQ problem.