Abstract
We discuss the construction of optimal servosystems with quadratic stability for uncertain systems with structured, time-invariant and bounded uncertainties. The aim is to design a control law such that the feedback system has three features: its output asymptotically tracks any constant reference input, it minimizes a certain quadratic performance index, thus inheriting the desirable properties of optimal regulator design, and the stability and the tracking property are both ensured for any uncertainty in a given bounded set. Based upon the observation that the quadratically stabilizing controller by Petersen, if exists, is an optimal regulator, in some way or another, for any of the uncertain system under consideration, such a control law together with a sufficient condition of its existence is derived. Further, by extending a particular optimal servosystem proposed by Suda and Ikeda to the uncertain system, it is shown that, under a sufficient condition, weaker than the so-called ‘matching condition’, it is possible to construct an optimal servosystem with quadratic stability which has a set of gain tuning parameters. Through an example, it is demonstrated that the speed of response is easily selected by adjusting these tuning parameters.
