caa a22 4500 445868600 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00498-011-0058-7 doi (NATIONALLICENCE)springer-10.1007/s00498-011-0058-7 Control systems on regular time scales and their differential rings [Elektronische Daten] [Zbigniew Bartosiewicz, Ülle Kotta, Ewa Pawłuszewicz, Małgorzata Wyrwas] The paper describes an algebraic construction of the inversive differential ring, associated with a nonlinear control system, defined on a nonhomogeneous but regular time scale. The ring of meromorphic functions in system variables is constructed under the assumption that the system is submersive, and equipped with three operators (delta- and nabla-derivatives, and the forward shift operator) whose properties are studied. The formalism developed unifies the existing theories for continuous- and discrete-time nonlinear systems, and accommodates also the case of non-uniformly sampled systems. Compared with the homogeneous case the main difficulties are noncommutativity of delta (nabla) derivative and shift operators and the fact that the additional time variable t appears in the definition of the differential ring. The latter yields that the new variables of the inversive closure, depending on t, have to be chosen to be smooth at each dense point t of the time scale. The Author(s), 2011 Time scale nationallicence Nonlinear system nationallicence Differential ring nationallicence Inversive closure nationallicence Bartosiewicz Zbigniew Faculty of Computer Science, Białystok University of Technology, Wiejska 45a, 15-351, Białystok, Poland aut Kotta Ülle Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia aut Pawłuszewicz Ewa Faculty of Mechanical Engineering, Białystok University of Technology, Wiejska 45c, 15-351, Białystok, Poland aut Wyrwas Małgorzata Faculty of Computer Science, Białystok University of Technology, Wiejska 45a, 15-351, Białystok, Poland aut Mathematics of Control, Signals, and Systems Springer-Verlag 22/3(2011-04-01), 185-201 0932-4194 22:3<185 2011 22 498 https://doi.org/10.1007/s00498-011-0058-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0058-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bartosiewicz Zbigniew Faculty of Computer Science, Białystok University of Technology, Wiejska 45a, 15-351, Białystok, Poland aut NATIONALLICENCE 700 1- Kotta Ülle Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia aut NATIONALLICENCE 700 1- Pawłuszewicz Ewa Faculty of Mechanical Engineering, Białystok University of Technology, Wiejska 45c, 15-351, Białystok, Poland aut NATIONALLICENCE 700 1- Wyrwas Małgorzata Faculty of Computer Science, Białystok University of Technology, Wiejska 45a, 15-351, Białystok, Poland aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 22/3(2011-04-01), 185-201 0932-4194 22:3<185 2011 22 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer