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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Introduction to Mathematical Systems Theory - A Behavioral Approach (Hardcover, 2nd Revised edition)
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Introduction to Mathematical Systems Theory - A Behavioral Approach (Hardcover, 2nd Revised edition)
Series: Texts in Applied Mathematics, v. 26
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This is a book about modelling, analysis and control of linear
time- invariant systems. The book uses what is called the
behavioral approach towards mathematical modelling. Thus a system
is viewed as a dynamical relation between manifest and latent
variables. The emphasis is on dynamical systems that are
represented by systems of linear constant coefficients. In the
first part of the book the structure of the set of trajectories
that such dynamical systems generate is analyzed. Conditions are
obtained for two systems of differential equations to be equivalent
in the sense that they define the same behavior. It is further
shown that the trajectories of such linear differential systems can
be partitioned in free inputs and bound outputs. In addition the
memory structure of the system is analyzed through state space
models. The second part of the book is devoted to a number of
important system properties, notably controllability,
observability, and stability. An essential feature of using the
behavioral approach is that it allows these and similar concepts to
be introduced in a representation-free manner. In the third part
control problems are considered, more specifically stabilization
and pole placement questions. This text is suitable for advanced
undergraduate or beginning graduate students in mathematics and
engineering. It contains numerous exercises, including simulation
problems, and examples, notably of mechanical systems and
electrical circuits.
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