Title :
On damped algebraic Riccati equations
Author :
He, C.Y. ; Hench, J.J. ; Mehrmann, V.
Author_Institution :
Dept. of Math., Kansas Univ., Lawrence, KS, USA
fDate :
11/1/1998 12:00:00 AM
Abstract :
In a recent paper, an algorithm was proposed which produces dampening controllers based on damped algebraic Riccati equations (DAREs) derived from a periodic Hamiltonian system. The solution to one of these DAREs is symmetric and the other is skew-symmetric; both of these solutions lead to a dampening feedback, i.e., a stable closed-loop system for which the real parts of the eigenvalues are larger in modulus than the imaginary parts. In this paper, the authors extend these results to include a broader class of damped algebraic Riccati equations which have Hermitian and skew-Hermitian solutions and show that every convex combination of these solutions produces a dampening feedback. This property can be used to vary the feedback with two parameters and thus obtain more flexibility in the controller design process
Keywords :
Riccati equations; closed loop systems; damping; eigenvalues and eigenfunctions; feedback; linear systems; matrix algebra; stability; state-space methods; closed-loop system; damped algebraic Riccati equations; dampening; eigenvalues; feedback; linear time invariant systems; matrix algebra; periodic Hamiltonian system; periodic Schur decomposition; stability; state space; Automatic control; Control systems; Observability; Optimized production technology; Process control; Riccati equations;
Journal_Title :
Automatic Control, IEEE Transactions on