Parameter Space Methods for Robust Control Design: A Guided Tour

Recently, there has been a renewed interest in the parameter space approach to control system analysis and design. The original concept has a long history starting in Russia by Vishnegradsky in 1876 and spreading throughout the world by the works of Neimark, Aizerman, Mitrovic, Meerov, Thaler, Seltzer, Ackermann, and many others. The parameter space approach has generally been viewed as an alternative to the classical methods of Routh-Hurwitz, Nyquist, Evans, Bode, and Nichols. When in the sixties the advent of the LQG theory of Kalman decreased the interest in classical design techniques, it almost diminished applications of the parameter methods. A recent widespread interest in robust design of control systems subject to structured perturbations shifted a considerable part of the research activity toward parameter space methods, and, at the same time, enlarged the scope of the approach to include the Liapunov's method as well as frequency domain concepts. The purpose of this paper is to review new and significant developments in the robust control design for structured (parametric) perturbations, which complement the large and well represented effort in robust design of control systems under structured and unstructured perturbations via frequency domain characterizations. A critical comparison of various parameter space concepts and methods is offered and examples are used to illustrate some of the differences between various results available at present. Directions for future research are suggested, which are motivated by applications as well as by utilization of modern computing technology. The paper is organized in three sections as follows.