Robust Finite-Dimensional Controller Synthesis

Abstract

In Chapter 7, we saw that the algebra $M\hat B\left( \beta \right)$ of infinite-dimensional transfer matrices is large enough to contain all β-exponentially stabilizable and detectable state linear systems with finite-rank inputs and outputs and many systems with unbounded input and output operators. In this chapter, we shall develop a theory for robust controllers for transfer matrices in $M\hat B\left( \beta \right)$, using the mathematical structure outlined in the last two chapters. First, we define the appropriate stability concepts for transfer matrices.