On controllability,near-controllability,controllable subspaces,and nearly-controllable subspaces of a class of discrete-time multi-input bilinear systems |
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| Affiliation: | 1. Dipartimento di Fisica e Astronomia, ‘G. Galilei’ & INFN, Università di Padova, Padova, Italy;2. Dipartimento di Neuroscienze, Università di Padova, Padova, Italy;3. Departments of Neurology, Radiology, Neuroscience, and Bioengineering, Washington University, School of Medicine, St. Louis, USA;4. Dipartimento di Ingegneria dell''informazione, Università di Padova, Padova, Italy;5. Dipartimento di Psicologia Generale, Università di Padova, Padova, Italy;6. Padova Neuroscience Center, Università di Padova, Padova, Italy;7. IRCCS San Camillo Hospital Foundation, Venice, Italy;1. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France;2. Faculty of Mathematics, “Alexandru Ioan Cuza” University, Bd. Carol I, no. 9-11, Iasi, Romania;1. Environment and Sustainability Institute, College of Engineering Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK;2. Centre for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK |
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| Abstract: | This paper considers a class of discrete-time multi-input inhomogeneous bilinear systems. The structure of such systems is most close to linear time-invariant systems’ but they own a strong property. That is, if the systems are uncontrollable, they can still be nearly controllable. Necessary and sufficient conditions for controllability and near-controllability of the systems are established by using a classical decomposition. Furthermore, a geometric characterization is given for the systems such that controllable subspaces and nearly-controllable subspaces are derived and characterized. Similar results on controllability are also obtained for the continuous-time counterparts of the systems. Finally, examples are provided to demonstrate the conceptions and results of this paper. |
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| Keywords: | Discrete-time bilinear systems Inhomogeneous systems Controllability Near-controllability Controllable subspaces Nearly-controllable subspaces |
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