The problem of robust stability for linear time-invariant single-output control systems subject to both structured (parametric) and unstructured (H/sub infinity /) perturbations is studied. A generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time-invariant dynamic system under perturbations of mixed type is presented. The solution involves calculating the H/sub infinity /-norm of a finite number of extremal plants. The problem of calculating the exact structured and unstructured stability margins is then constructively solved. A feedback control system containing a linear time-invariant plant which is subject to both structured and unstructured perturbations is considered. The case where the system to be controlled is interval is treated, and a nonconservative, easily verifiable necessary and sufficient condition for robust stability is given. The solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered.
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机译:研究了线性时不变单输出控制系统在结构(参数)和非结构(H / sub infinity /)扰动下的鲁棒稳定性问题。提出了小增益定理的推广,为混合时滞摄动下线性时不变动力系统的鲁棒稳定性提供了充要条件。该解决方案涉及计算有限数量的极值植物的H / sub无限大/范数。然后,建设性地解决了计算精确的结构化和非结构化稳定裕度的问题。考虑一种包含线性时不变设备的反馈控制系统,该设备会同时受到结构性和非结构性摄动的影响。处理了要控制的系统是间隔的情况,并给出了非保守,易于验证的必要和充分条件,以实现稳定的稳定性。该解决方案基于工厂参数空间中有限数量的线段的工厂参数属性中有限数量的线段的极值,沿着该极值会遇到最接近不稳定性的点。
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