Guaranteed Cost Control Problem

Introduction

In the previous chapter, we presented different results that can be used to deal with nominal and uncertain systems and also with systems that are subject to external disturbances. LMI conditions were developed to design controller to achieve the desired goal. In this chapter we consider uncertain discrete-time with norm bounded uncertainties and try to present results that can be used to design a controller such that the resulting closed-loop system is asymptotically stable while an upper bound on the closed-loop value of the associated linear quadratic cost function is guaranteed.