Title

The symplectic semigroup and Riccati differential equations

Document Type

Article

Publication Date

1-1-2006

Abstract

In this paper, we study close connections that exist between the Riccati operator (differential) equation that arises in linear control systems and the symplectic group and its subsemigroup of symplectic Hamiltonian operators. A canonical triple factorization is derived for the symplectic Hamiltonian operators, and their closure under multiplication is deduced from this property. This semigroup of Hamiltonian operators, which we call the symplectic semigroup, is studied from the viewpoint of Lie semigroup theory, and resulting consequences for the theory of the Riccati equation are delineated. Among other things, these developments provide an elementary proof for the existence of a solution of the Riccati equation for all t ≥ 0 under rather general hypotheses. © 2006 Springer Science+Business Media, Inc.

Publication Source (Journal or Book title)

Journal of Dynamical and Control Systems

First Page

49

Last Page

77

This document is currently not available here.

Share

COinS