Title :
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
fDate :
4/1/2004 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2004.825628
