Monotone dynamical systems, graphs, and stability of large scale interconnected systems [Elektronische Ressource] / von Björn Sebastian Rüffer

Bj¨ orn S. Ruffer¨Monotone dynamical systems, graphs, and stability oflarge-scale interconnected systemsMonotone dynamical systems,graphs, and stability of large-scaleinterconnected systemsvon Bjorn¨ Sebastian Ruffer¨Dissertation zur Erlangung des Grades eines Doktorsder Naturwissenschaften– Dr. rer. nat. –Vorgelegt im Fachbereich 3(Mathematik & Informatik)der Universit¨ at Bremenim August 2007Datum des Promotionskolloquiums: 19. September 2007Gutachter: Prof. Dr. Fabian Wirth (Universit¨ at Wurzburg)¨Prof. Dr. Lars Grune¨ (Universit¨ at Bayreuth)To my parents, Antje and Herbert.ContentsIntroduction 11. Preliminaries 91.1.Comparisonfunctions...................... 91.2.Orderandmonotonicity 121.2.1.Order........................... 121.2.2.Monotonicity....................... 141.2.3.Matrixinducedoperators................ 161.3.Graphsandprojections 181.4.Dynamicalsystems........................ 221.5. Sets of decay and the “no joint increase” condition . . . . . . 251.6.Notesandreferences 312. Monotone dynamics 332.1.Fromattractivitytoorder.................... 342.2.Fromordertoatractivity 382.3.Pathconstruction......................... 442.4.Dichotomyintwodimensions.................. 632.5. Monotone inequalities, solutions, and bounds on solutions . . 662.6.AlocalversionofTheorem2.5.1................ 742.7.Notesandreferences....................... 763. Input-to-output stability for interconnected systems 793.1.Stabilityconcepts 833.1.1.