Minimal state space realisation of continuous-time linear time-variant input–output models. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Goos, J.; Pintelon, R.
• Is Part Of: International journal of control. Volume 89:Issue 4(2016)
• Page Start: 722
• Page End: 730
• Publication Date: 2016-04-02
• Subjects: Time-varying systems -- realisation theory -- system identification; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2015.1094828
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In the linear time-invariant (LTI) framework, the transformation from an input–output equation into state space representation is well understood. Several canonical forms exist that realise the same dynamic behaviour. If the coefficients become time-varying however, the LTI transformation no longer holds. We prove by induction that there exists a closed-form expression for the observability canonical state space model, using binomial coefficients.