Geometric minimization under external equivalence for implicit descriptions

✍ Scribed by Moisés E. Bonilla; Michel Malabre

• Book ID: 102992091
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 523 KB
• Volume: 31
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(94)00175-i

✦ Synopsis

We consider mmimality under external equivalence for linear. time-invariant. implicit (E, A. B. C) descriptions of the type .G(r) = Ax(!) + Bu(t). ,v(t) = Cx(f). Necessary and sufficient conditions for external minimaiity have been previously given, from an algebraic point of view by Kuijper. We propose here alternative geometric characterizations, as well as a geometric reduction procedure that extracts. from a given (E, A. B. C) description. a minimal model of the same type. We also geometrically characterize. in terms of the geometry of (E. A. B. C). the corresponding minimal dimensions for the state space and for the state equation space.