Parameter space methods for robust control design: a guided tour

The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed. Both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared. In the context of algebraic methods, most promising are the Kharitonov-type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space, maximizing its size using minimax or some other mathematical programming technique. In the framework of Lyapunov's direct method, the dominant approach has been a quadratic function estimation of stability regions in the parameter space. In large-sale systems, the concept of vector Lyapunov functions has been used with the possibility of choosing quadratic forms, norm-like functions, and their combinations.>