2011/11/10 by Rudolf Rupp, Rupp, Rudolf, Amol Sasane +1
Mathematics · Physics and Astronomy · #46J15 (Secondary) #93B36 (Primary) 93D15 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #math.CV #math.FA #math.OC #msc:46J15 #msc:93B36 #msc:93D15
paper · pdf · doi:10.48550/arxiv.1111.2467
13 pages, 0 figures
arxiv created 2011/11/10 · openalex publication_date 2011/11/10 · arxiv updated 2011/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A+ be the ring of Laplace transforms of complex Borel measures on R with support in [0,+∞) which do not have a singular nonatomic part. We compare the nu-metric dA+ for stabilizable plants over A+ given in the article by Ball and Sasane [2010], with yet another metric dH^∞|A+, namely the one induced by the metric dH^∞ for the set of stabilizable plants over H^∞ given in teh article by Sasane in 2011. Both dA+ and dH^∞ coincide with the classical Vinnicombe metric defined for rational transfer functions, but we show here by means of an example that these two possible extensions of the classical nu-metric for plants over A+ do not coincide on the set of stabilizable plants over A+. We also prove that they nevertheless give rise to the same topology on stabilizable plants over A+, which in turn coincides with the gap metric topology.