9508620 Bose The spark generated by Kharitonov's result on root clustering of interval polynomials has influenced the robust control field in a significant manner in a relatively short time. The property studied in the setting of Kharitonov theory and its various generalizations is primarily concerned with robust stability of continuous-time and discrete-time one dimensional systems and, to a lesser extent, multidimensional systems. The achieving of robust stability is crucial in the design of control systems when a plant, possibly of high order and with uncertain parameters present is targeted for stabilization by a low order compensator. In the control of flexible large space structures such as solar power satellites and orbiting telescopes, for example, the objective is to achieve robust control of a plant of high order with a controller of lower order. Robust control is necessary because of elastic mode truncation (modelling error) and parameter uncertainty. The effect of mode truncation is possible instability due to the incorporated either in the plant transfer matrix representation or the state-space representation. Usually, the coefficient perturbations will not be independent of each other so that the Kharitonov-type results, if used without any modification, would have the advantage of simplicity in application but the disadvantage of yielding only sufficient conditions, which may not be as tight as desired for robust stability. Furthermore, though robust stability is crucial to performance evaluation of control systems, other measures of performance like robust frequency response, robust pole placement, and minimax control or rate feedback systems are necessary in important applications like control of large space structures. ***
