2 Elements of Descriptor Systems Theory.

In this chapter we summarize some basic definitions and preliminary results that will be used throughout this book. Most of the treatments are purely algebraic and the definitions are fairly standard. In particular, we give a generalized version of the LaSalle’s Invariance Principle, which is useful in the proof of internal stability in the subsequent chapters. Furthermore, Bounded Real Lemma, which is a basic tool for solving the $\mathcal{H}•\infty$ control problems, is extended to the descriptor systems in a natural way. [ABSTRACT FROM AUTHOR]