First Advisor

Gerardo Lafferriere

Term of Graduation

Spring 2007

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences






Control theory, Hybrid computers, Polyhedral functions, System analysis



Physical Description

1 online resource (vi, 110 pages)


Hybrid Control Systems are increasingly investigated as models for control systems where the interaction between continuous and discrete processes is tightly integrated. As yet, there is no general agreement as to what constitutes a canonical hybrid system. Rather various subclasses of systems combining continuous evolution and discrete event characteristics are analyzed for each application. In this dissertation we first unify the presentation of hybrid systems with a rich model which encompasses most examples of interest. We classify the available results and show how they fit together within the different subcategories. In the main part of the dissertation we prove that for piecewise linear control systems---introduced over twenty years ago---the isomorphism problem is decidable in polynomial time in the number of inequalities defining the sets and the dimension of the sets. We also prove a stability result for switching systems arising from the problem of vehicle formations.


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