3. The Behavioral Paradigm

In this chapter, we introduce basic concepts of the behavioral approach that put the foundation to address active FTC approaches in this book. We shall see here how the behaviors are described for a dynamical system. The elementary properties (for example linearity, time/shift invariance) associated with a dynamical system are discussed taking this behavioral point of view. As we mentioned (very briefly) in the last chapter, the real essence of this approach lies in its representation-free description. However, for the brevity of explanation, we shall often utilize kernel representations. These representations consider the polynomial matrices for describing a system, which are considered more general way of representing dynamical systems since these representations can easily be translated into either external-type or internal-type of representations by Chen (Linear systsem theory and design. Oxford University Press, New York, 1999, [18, Sects. 6–7]), Polderman and Willems (Introduction to mathematical systems theory: a behavioral approach. Springer, Berlin, 1997, [84]). To motivate further use of behavioral framework, we have considered various follow-up examples.