Introduction to mathematical systems theory

the long version

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 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. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, specifically stabilization and pole placement questions. This text is suitable for advanced undergraduate or beginning undergraduate students in mathematics and engineering. It contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.