Robust Performance: Multi-Dimensional Systems Approach

9508620 Bose Kharitonov关于区间多项式根聚类的结果所产生的火花在较短的时间内对鲁棒控制域产生了显著的影响。在Kharitonov理论及其各种推广的背景下研究的性质主要涉及连续时间和离散时间一维系统的鲁棒稳定性，在较小程度上涉及多维系统。在控制系统设计中，当目标对象可能是高阶且参数不确定时，实现鲁棒稳定性是至关重要的。在太阳能卫星、轨道望远镜等柔性大空间结构的控制中，目标是用低阶控制器实现对高阶对象的鲁棒控制。由于弹性模态截断（建模误差）和参数的不确定性，需要进行鲁棒控制。模式截断的影响可能是不稳定的，这是由于在植物转移矩阵表示或状态空间表示中加入了模式截断。通常情况下，扰动系数不会相互独立，因此，如果不加任何修改地使用kharitonov型结果，将具有应用简单的优点，但缺点是只产生充分条件，这些条件可能不像鲁棒稳定性所期望的那样严格。此外，尽管鲁棒稳定性对控制系统的性能评估至关重要，但在大型空间结构控制等重要应用中，鲁棒频率响应、鲁棒极点放置、极大极小控制或速率反馈系统等其他性能度量也是必要的。＊＊＊

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. ***