ABSTRACT
Control theory deals with analysis of dynamical systems and methodologies to construct controllers. The object to be controlled can be modeled in several ways. Basic concepts, like feedback, performance, stability, sensitivity, etc., are quite general, but techniques and tools vary with the type of models used. A typical first course in control covers continuous time systems described by linear systems with one input and one output (Single-Input-Single-Output, SISO, systems). In this book we assume the reader to be familiar with this basic theory, including frequency domain analysis and simple state-space representations. The aim of the book is to extend this theory to cover
• Multivariable systems (multiple inputs and multiple outputs, MIMO)
• Discrete time theory
• Nonlinear systems
For SISO systems we will also convey a deeper understanding of the fundamental performance limitations that may be at hand. To motivate the ensuing treatment, we start by considering two examples, where the behavior cannot be understood from linear SISO theory. Later in this introductory chapter we will treat some general issues in control, like the role of discrete and continuous time models (Section 1.3), list the basic concepts and notations (Section 1.4), and discuss general aspects of stability and signal sizes (Sections 1.5 and 1.6).
