IJPAM: Volume 38, No. 3 (2007)

THE DUALITIES OF LYAPUNOV AND RICCATI MATRICES
IN LINEAR QUADRATIC CONTROL THEORY

Chein-Shan Liu
Department of Mechanical and Mechatronic Engineering
National Taiwan Ocean University
Keelung, 202-24, TAIWAN, R.O.C.
e-mail: csliu@mail.ntou.edu.tw


Abstract.The properties of linearly quadratically controlled systems with complete state are crystallized in the canonical relations of symplecticity. The dualities of the Lyapunov matrices and the Riccati matrices are all derived from the symplectic relations. The complete state controller is shown to be superior, as the optimality indicates, to the conventional state feedback controller. The performance improvement is derived analytically with a quantitative formula.

Received: April 11, 2007

AMS Subject Classification: 93B52, 93C05

Key Words and Phrases: active control, linear quadratic optimal control, Hamiltonian matrix, Riccati matrix, Lyapunov matrix, canonical symplectivity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 3