Applications of geometric control: Constrained systems and switched systems

Mustafa Kaba

Research output: ThesisThesis fully internal (DIV)

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Abstract

After a formal introduction to the content of the thesis in the first chapter, in Chapter 2 we take up the controllability problem for discrete-time linear systems with convex conic output constraints. We provide an almost complete characterization of controllability for discrete-time linear systems with convex conic constraints.
In Chapter 3 we discuss the controllability problem of Chapter 2 in absence of the conicity assumption. We further generalize the results of Chapter 2 and show that the setting we proposed for the analysis of constrained linear systems is extremely efficient in this more general case too. Hence, we manage to provide a spectral characterization of controllability for discrete-time linear systems with convex output constraints, which covers all previously known results on the subject.
Chapter 4 is dedicated to the discussion of controllability for discrete-time conewise linear systems. The results of Chapter 2 become handy in the analysis. We provide algebraic necessary and sufficient conditions which guarantee that the convex hull of the reachable set of the discrete-time conewise linear system is the whole state space.
Chapter 5 focuses on the left-invertibility problem for continuous-time switched linear systems. We take a geometric approach to provide necessary and sufficient conditions that are linear and hence can be checked easily.
The thesis ends with the sixth chapter, which hosts the concluding remarks.
Translated title of the contributionToepassingen van geometrische controle: Systemen met een beperkte en geschakelde systemen
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Groningen
Supervisors/Advisors
  • Camlibel, Kanat, Supervisor
Award date19-Sep-2014
Place of Publication[S.l.]
Publisher
Print ISBNs978-90-367-7222-8
Electronic ISBNs978-90-367-7221-1
Publication statusPublished - 2014

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