Title :
Balancing transformations for unstable nonminimal linear systems
Author :
Therapos, Constantine P.
Author_Institution :
Dept. of Electr. Eng., Nat. Tech. Univ. of Athens, Greece
fDate :
4/1/1989 12:00:00 AM
Abstract :
It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Λ. If, in addition, the eigenvalues of A , say λ, satisfy the relation λi+λ j≠0(λiλj≠1) then the matrix Λ will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained
Keywords :
controllability; eigenvalues and eigenfunctions; linear systems; matrix algebra; observability; controllability; eigenvalues; observability; real diagonal matrix; unstable nonminimal linear systems; Control system synthesis; Controllability; Digital filters; Eigenvalues and eigenfunctions; Equations; Linear systems; Noise reduction; Observability; Reduced order systems; Yttrium;
Journal_Title :
Automatic Control, IEEE Transactions on
