Systems and Control

Credits	6 credit points
Instructors	Trentelman, H.L. (Rijksuniversiteit Groningen), Polderman, J.W. (Universiteit Twente), Stoorvogel, A.A. (Universiteit Twente)
E-mail	h.l.trentelman@math.rug.nl, j.w.polderman@math.utwente.nl, a.a.stoorvogel@math.utwente.nl
Aim	Mathematical systems theory is concerned with problems related to dynamic phenomena in interaction with their environment. These problems include: Modeling. Obtaining a mathematical model that reflects the main features. A mathematical model may be represented by difference or differential equations, but also by inequalities, algebraic equations, and logical constraints. Analysis and simulation of the mathematical model. Prediction and estimation. Control. By choosing inputs or, more general, by imposing additional constraints of the system may be influenced so as to obtain certain desired behavior. The aim of the course is to become familiar with the basic concepts and more advanced notions of the mathematical theory of systems and control.
Description	Linear time-invariant differential systems, algebraic representation of dynamical systems using polynomial matrices. Minimal representations. Autonomous systems. State space models and the Markov property. Nonlinear systems and linearization. Controllability and observability. Latent variable models. Stability of state space models. Stabilization by state feedback and by dynamic feedback. Basic observer theory and its relation to filter theory. Transfer matrices and the connection with state space models and behaviors. Poles of transfer matrices and the connections with internal stability and input-output stability. Injective and surjective dynamic systems and the connection to invertibility. Zeros of transfer matrices and the connection to invertibility of dynamic systems. Relationship with tracking problems. Zero-dynamics and minimum-phase systems. Connections with unstable pole-zero cancellation and the problems of infinite zeros.
Organization	This is an intensive course. For information about the organization see also 'Courses & Exams'.
Examination	Homework and final presentation.
Literature	Introduction to Mathematical Systems theory: a Behavioral Approach, by J.W. Polderman and J.C. Willems (Springer, New York, 1998). Additional lecture notes will be handed out during the course. NOTE: The book mentioned above is sold out and will not be available before Spring 2007. Fortunately, you can download this book at http://wwwhome.math.utwente.nl/~poldermanjw/onderwijs/DISC/mathmod/book.pdf

Last changed: 18-01-2012 10:21