On the solvability of extended Riccati equations

Author

Barabanov, Nikita E. ; Ortega, Romeo

Author_Institution

Dept. of Math., North Dakota State Univ., Fargo, ND, USA

Volume

49

Issue

4

fYear

2004

fDate

4/1/2004 12:00:00 AM

Firstpage

598

Lastpage

602

Abstract

The Kalman-Yakubovich-Popov lemma, which gives necessary and sufficient conditions for solvability of matrix Lur´e-Riccati equations, is a milestone in modern control theory. There are, however, important and general extensions of this lemma that have not been studied yet. Starting with the absolute stability theory with semidefinite frequency domain function, we generalize here this lemma to the sign indefinite case-a research that is motivated by new problems on passivity and H_∞ control theory.

Keywords

H^∞ control; Riccati equations; absolute stability; computability; eigenvalues and eigenfunctions; matrix algebra; nonlinear control systems; H_∞ control theory; Hamiltonian matrix; Kalman-Yakubovich-Popov lemma; Kronecker blocks; Lagrangian subspaces; Lur´e-Riccati equations; absolute stability theory; eigenvalues; frequency domain function; matrix equations; maximal invariant orthogonal subspace; nonlinear systems; passivity problems; solvability; spectral factorization; Computational modeling; Control theory; Costs; Nonlinear equations; Process control; Riccati equations; Stability; Steady-state; Stochastic processes; System performance;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2004.825628

Filename

1284725