The motivation for this proposal is derived from the problem of robust control in the presence of structured real uncertain parameters. More specifically, it deals exclusively with linear systems described by a transfer function or state space model which includes uncertain parameters entering into various plant coefficients. The takeoff point for research is the body of literature motivated by Kharitonov's Theorem. Given the fact that this body of literature deals almost exclusively with robust stability analysis, the first focal point of the research is synthesis of robust stabilizing controllers. A spark for this line of work is provided by some recent extreme point results (involving the PI) on robust stabilization of an interval plant (ratio of interval polynomials) with a first order controller. Additional motivation is also provided by the so-called value set approach. Given the widespread use of value sets in an analysis context, the open question is: To what extent are value sets useful in a synthesis context? The second focal point of this proposal is robust performance. That is, the objective is to deal with robust performance specifications over and above stability. Analogous to the investigation of robust stabilization, the intention is to begin the work by looking at robust performance problems with low order controllers and then to follow up with the higher order case. In this framework, a number of important research problems are proposed. The third and final focal point is described by the words generating mechanism. That is, to enlarge the class of uncertainties which can be accommodated, it is proposed to impose more structure on the "uncertain" polynomials and rational functions which arise in the analysis.
