caa a22 4500 467932298 CHVBK 20180406152947.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s00020-003-1356-3 doi (NATIONALLICENCE)springer-10.1007/s00020-003-1356-3 Conservative State-Space Realizations of Dissipative System Behaviors [Elektronische Daten] [Joseph Ball, Olof Staffans] Abstract.: It is well known that a Schur-class function S (contractive operator-valued function on the unit disk) can be realized as the transfer function S(z)=D+zC(I−zA)−1B of a conservative discrete-time linear system (x(n+1)=Ax(n)+Bu(n), y(n)=Cx(n)+Du(n) with $$ U = \left[ {\begin{array}{*{20}l} A & B\\ C & D\end{array}} \right]$$ unitary). One method of proof of this result (the "lurking isometry” method) identifies a solution U of the problem as a unitary extension of a partially defined isometry V determined by the problem data. Reformulated in terms of the graphs of V and U, solutions are identified with embeddings of an isotropic subspace of a certain Krein space $$\mathcal{K}$$ constructed from the problem data into a Lagrangian subspace (maximal isotropic subspace of $$\mathcal{K}$$ ). The contribution here is the observation that this reformulation applies to other types of realization problems as well, e.g., realization of positive-real or J-contractive operator-valued functions over the unit disk (respectively over the right half plane) as the transfer function of a discrete-time (respectively, continuous-time) conservative system, i.e., an input-state-output system for which there is a quadratic storage function on the state space for which all system trajectories satisfy an energy-balance equation with respect to the appropriate supply rate on input-output pairs. The approach allows for unbounded state dynamics, unbounded input/output operators and descriptor-type state-space representations where needed in a systematic way. These results complement recent results of Arov-Nudelman, Hassi-de Snoo-Tsekanovskii, Belyi-Tsekanovskii and Staffans and fit into the behavioral frameworks of Trentelman-Willems and Georgiou-Smith. Birkhäuser Verlag, Basel, 2006 Energy balance nationallicence scattering-conservative nationallicence impedance-conservative nationallicence discrete and continuous time nationallicence distributed-parameter system nationallicence Ball Joseph Department of Mathematics, Virginia Tech, 24061-0123, Blacksburg, Virginia, USA aut Staffans Olof Department of Mathematics, Åbo Akademi University, FIN-20500, Åbo, Finland aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/2(2006-02-01), 151-213 0378-620X 54:2<151 2006 54 20 https://doi.org/10.1007/s00020-003-1356-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-003-1356-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ball Joseph Department of Mathematics, Virginia Tech, 24061-0123, Blacksburg, Virginia, USA aut NATIONALLICENCE 700 1- Staffans Olof Department of Mathematics, Åbo Akademi University, FIN-20500, Åbo, Finland aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/2(2006-02-01), 151-213 0378-620X 54:2<151 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer