We introduce two "polynomial invariants" for rooted trees and discuss their properties. A statistical mechanics interpretation is pointed out. In particular, we show that the partition function of the Ising model, in the simple surface separation ensemble, is a complete invariant.
Feedback invariants of restrictions — a polynomial approach
✍ Scribed by I. Zaballa
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 192 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0005-1098
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✦ Synopsis
The possible feedback invariants of a linear time-invariant dynamical system, represented by a pair of matrices (A, B), are studied when the only information about the system is that it has an (A, B)-invariant subspace, S, whose restriction is an autonomous system and the quotient is controllable. This problem is shown to be related to the problem of designing a control matrix B for a series connected system to have prescribed feedback invariants.
📜 SIMILAR VOLUMES
The paper is an attempt to solve the problem of row-by-row decoupling in its full generality. The presented polynomial setting gives a deeper insight into the problem and provides a computational procedure.