基于广义界实定理的窗口H_∞性能分析

Window H_∞ performance analysis based on generalized bounded real theorem

为研究连续时间控制系统局部频段的H∞性能,基于传统H∞范数提出了窗口H∞范数的新概念,指出传统H∞范数是窗口H∞范数的特例.利用广义Kalman-Yakubovich-Popov引理证明了弱形式广义界实定理,针对低频段、中频段、高频段3种情况得出了相应的研究结果.低频段的推论能应用于控制系统的带宽设计问题,中频段的推论能用于控制系统的稳定裕度指标设计问题,高频段的推论能用于控制系统抗干扰的设计问题.例子表明窗口H∞性能分析方法比传统H∞性能分析方法更适于局部频段.

To investigate H∞ performance of continuous-time control systems in local frequency range, a new conception of window H∞ norm is presented based on traditional H∞ norm, and it is stated that traditional H∞ norm is a special case of window H∞ norm. Weak form generalized bounded real theorem is proved using generalized Kalman-Yakubovich-Popov lemma. The relevant results are obtained for three cases including low frequency range, middle frequency range and high frequency range. The corollary in low frequency range can be applied to bandwidth design problem of control systems, and the corollary in middle frequency range can be applied to stability margin design problem of control systems, and the corollary in high frequency range can be applied to anti-disturbance design problem of control systems. The example demonstrates that the method of window H∞ performance analysis is more suitable for local frequency range than the traditional H∞ performance anaysis method.