An Introduction to Mathematical Systems Theory: A Behavioral Approach 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 coefficient differential equations.
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.
The 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.