Title :
On the exponential convergence of the time-invariant matrix Riccati differential equation
Author :
Callier, Frank M. ; Winkin, Joseph ; Willems, Jacques L.
Author_Institution :
Dept. of Math., Fac. Univ. Notre Dame de la Paix, Namur, Belgium
Abstract :
The exponential nature of the convergence of the solution of the time-invariant matrix Riccati differential equation toward the stabilizing solution of the algebraic Riccati equation is displayed on an explicit formula. It is assumed that the system is stabilizable and the Hamiltonian matrix has no eigenvalues on the imaginary axis. Computable characteristics are given which can be used to estimate how well a large finite horizon linear-quadratic (LQ) problem is approximated by an infinite horizon LQ problem
Keywords :
convergence; differential equations; matrix algebra; optimal control; Hamiltonian matrix; algebraic Riccati equation; exponential convergence; finite horizon linear quadratic problem; infinite horizon linear quadratic problem; optimal control; stabilizing solution; time-invariant matrix Riccati differential equation; Closed loop systems; Convergence; Differential algebraic equations; Differential equations; Eigenvalues and eigenfunctions; Infinite horizon; Mathematics; Optimal control; Riccati equations; Symmetric matrices;
Conference_Titel :
Decision and Control, 1992., Proceedings of the 31st IEEE Conference on
Conference_Location :
Tucson, AZ
Print_ISBN :
0-7803-0872-7
DOI :
10.1109/CDC.1992.371477
