Duality of switched DAEs. Issue 3 (September 2016)

• Record Type: Journal Article
• Authors: Küsters, Ferdinand; Trenn, Stephan
• Is Part Of: Mathematics of control, signals, and systems. Volume 28:Issue 3(2016)
• Page Start: 1
• Page End: 35
• Publication Date: 2016-09
• Subjects: Duality -- Switched systems -- Differential-algebraic equations; Control theory -- Periodicals; Signal processing -- Periodicals; System analysis -- Periodicals; 621.38223
• DOI: 10.1007/s00498-016-0177-2
• Languages: English
• ISSNs: 0932-4194

Abstract

Abstract We present and discuss the definition of the adjoint and dual of a switched differential-algebraic equation (DAE). For a proper duality definition, it is necessary to extend the class of switched DAEs to allow for additional impact terms. For this switched DAE with impacts, we derive controllability/reachability/determinability/observability characterizations for a given switching signal. Based on this characterizations, we prove duality between controllability/reachability and determinability/observability for switched DAEs.