Energy functions for dissipativity-based balancing of discrete-time nonlinear systems |
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| Authors: | Ricardo Lopezlena Jacquelien M A Scherpen |
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| Affiliation: | (1) Department of Mathematics, Missouri Southern State University, Joplin, MO 64801, USA;(2) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA;(3) Department of Mathematics, The University of Georgia, Athens, GA 30602, USA;(4) Department of Systems Engineering, Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, 0200, Australia |
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| Abstract: | Most of the energy functions used in nonlinear balancing theory can be expressed as storage functions in the framework of dissipativity theory. By defining a framework of discrete-time dissipative systems, this paper presents existence conditions for their discrete-time energy functions along with algorithms to find them based on dynamic optimization problems. Furthermore, the important case of the nonlinear discrete-time versions of the controllability and observability functions, its properties and algorithms to find them are presented. These algorithms are illustrated with linear and nonlinear examples. |
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