Linear passive systems and maximal monotone mappings

• Published in: Mathematical programming Vol. 157; no. 2; pp. 397 - 420
• Main Authors: Camlibel, M. K., Schumacher, J. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Collaboration; Combinatorics; Convex analysis; Differential equations; Dynamical systems; Full Length Paper; Inclusions; Interconnection; Linear systems; Mapping; Mathematical analysis; Mathematical and Computational Physics; Mathematical functions; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Partial differential equations; Passivity; Studies; System theory; Theoretical; Uniqueness; 47H05; 93C05; 34A60; 34A12; 90C33; 47H04
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-015-0945-7

This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is passive and the static relation is maximal monotone. Based on the classical results on such differential inclusions, we conclude that such interconnections are well-posed in the sense of existence and uniqueness of solutions. Finally, we investigate conditions which guarantee well-posedness but are weaker than passivity.