Orbits of controllable and observable systems
Let a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a realization of a prescribed transfer function matrix can be represented by triples of matrices $(A,B,C)$. The permitted transformations of basis changes in the spa...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 1999 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1049 |
| Online Access: | https://hdl.handle.net/2117/1049 |
| Access Level: | Open access |
| Keyword: | System theory Algebras, Linear Multilinear algebra Matrices Controllability Observability Lie group action Orbits Sistemes, Teoria de Àlgebra lineal Àlgebra multilineal Matriu S, Teoria Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure |
| Summary: | Let a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a realization of a prescribed transfer function matrix can be represented by triples of matrices $(A,B,C)$. The permitted transformations of basis changes in the space state on the systems can be seen in the space of triples of matrices as similarity equivalence. In this paper we give a geometric characteriaztion of controllable and observable systems as orbits under a Lie group action. As a corollary we obtain a lower bound of the distance between a controllable and observable triple and the nearest uncontrollable one. |
|---|