Balancing transformations for unstable nonminimal linear systems
- 1 April 1989
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 34 (4) , 455-457
- https://doi.org/10.1109/9.28023
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 + λj ≠ 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 obtainedKeywords
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