Robust Performance: Multi-Dimensional Systems Approach

小行星9508620 Kharitonov关于区间多项式的根聚类的结果所产生的火花在相对较短的时间内以显著的方式影响了鲁棒控制领域。 在Kharitonov理论及其各种推广的背景下研究的属性主要涉及连续时间和离散时间一维系统的鲁棒稳定性，并在较小程度上涉及多维系统。 在控制系统设计中，当一个对象，可能是高阶的，并且具有不确定的参数，需要通过低阶补偿器来稳定时，鲁棒稳定性的实现是至关重要的。 例如，在诸如太阳能卫星和轨道望远镜的柔性大型空间结构的控制中，目标是用低阶控制器实现高阶对象的鲁棒控制。 由于弹性模态截断（建模误差）和参数不确定性，鲁棒控制是必要的。 模态截断的影响是可能的不稳定性，由于被控对象的传递矩阵表示或状态空间表示。 通常，系数扰动将不是彼此独立的，使得Kharitonov型结果，如果不作任何修改使用，将具有应用简单的优点，但仅产生充分条件的缺点，这可能不像鲁棒稳定性所期望的那样严格。 此外，虽然鲁棒稳定性是至关重要的性能评估的控制系统，其他措施的性能，如鲁棒频率响应，鲁棒极点配置，极小极大控制或速率反馈系统是必要的，在重要的应用，如大型空间结构的控制。 ***

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. ***