STABILIZATION OF PERTURBED SYSTEMS VIA LINEAR OPTIMAL REGULATOR

Linear quadratic state feedback regulators make the resulting closed-loop systems stable enough, i. e. they realize robust stabilization. Many attempts at robust stabilization using linear quadratic regulators have been reported. One of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms, i. e. nominal values and the deviation from them. In this paper, it is assumed that the upper and lower bounds for each uncertain parameter can be estimated. This enables us to dispense with nominal values. The main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds. The systems under consideration are therefore those having interval system matrices. A certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the same feedback law remains so for systems with system matrices whose entries are all possible combinations of the endpoints of their variation range.