Bounding the distance of a controllable and observable system to an uncontrollable or unobservable one
Let $(A,B,C)$ be a triple of matrices representing a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ under similarity equivalence, corresponding to a realization of a prescribed transfer function matrix. In this paper we measure the dis...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 1999 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1048 |
| Acesso em linha: | https://hdl.handle.net/2117/1048 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Algebras, Linear Multilinear algebra Matrices System theory Linear Systems Controllability measure Observability measure Distance to uncontrollable and unobservable Àlgebra lineal Àlgebra multilineal Matriu S, Teoria Sistemes, Teoria de Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure |
| Resumo: | Let $(A,B,C)$ be a triple of matrices representing a time-invariant linear system $\left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ under similarity equivalence, corresponding to a realization of a prescribed transfer function matrix. In this paper we measure the distance between a irreducible realization, that is to say a controllable and observable triple of matrices $(A,B,C)$ and the nearest reducible one that is to say uncontrollable or unobservable one. Different upper bounds are obtained in terms of singular values of the controllability matrix $C(A,B,C)$, observability matrix $O(A,B,C)$ and controllability and observability matrix $CO(A,B,C)$ associated to the triple. |
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