Stabilizing Controllers

Abstract

In this chapter, our focus is on plant and controller descriptions. The minimum requirement is that any practical controller stabilizes or maintains the stability of the plant. We set the stage with various mathematical representations, also termed models, for the plants to be controlled. Our prime focus is on discrete-time, linear, finite-dimensional, dynamical system representations in terms of state space equations and (matrix) transfer functions; actually, virtually all of the results carry over to continuous time, and indeed time-varying systems as discussed in Chapter 8. A block partition notation for the system representations is introduced which allows for ready association of the transfer function with the state space description of the plant. It proves convenient to develop dexterity with the block partition notation. Manipulations such as concatenation, inverse, and feedback interconnection of systems are easily expressed using this formalism. Controllers are considered with the same dynamical system representations.