论文标题
超级奇异值的计算和SISO时间延迟系统的强h-界数规范
Computation of Extremum Singular Values and the Strong H-infinity Norm of SISO Time-Delay Systems
论文作者
论文摘要
我们考虑了单输入单输出（SISO）时间延迟系统的H-赋值规范的计算，该系统用延迟差分代数方程来描述。与文献中的迭代级别集方法不同，我们提出了一种计算H-赋值标准的新型数值方法。此方法需要解决一个特征值问题，最多是在级别设置方法的每种迭代中，最多是特征值问题的两倍，但实际上通常要低得多。我们首先表明，转移函数极端的计算可以转变为先验函数的虚轴零的计算。我们通过预测 - 校正型算法计算这些零。众所周知，可以对智障和中性类型系统进行建模的延迟差分代数系统的H-界限规范，对于任意较小的延迟扰动，可能是敏感的。最近，这导致了强大的H-赋值规范的概念，该规范明确考虑了如此小的延迟扰动。我们提出了一种直接的数值方法，用于计算SISO Time-Delay系统的强h-界限规范。我们的算法适用于时间延迟系统和/或控制器的互连（系列，并行，反馈，连接）的闭环系统。
We consider the computation of H-infinity norms for Single-Input-Single-Output (SISO) time-delay systems, which are described by delay differential algebraic equations. Unlike the iterative level set methods in the literature, we present a novel numerical method to compute the H-infinity norm. This method requires solving one eigenvalue problem of at most twice the size of the eigenvalue problem in every iteration of a level set method, but in practice often considerably lower. We first show that the computation of extrema of the transfer function can be turned into the computation of the imaginary axis zeros of a transcendental function. We compute these zeros by a predictor-corrector type algorithm. It is known that the H-infinity norm of delay differential algebraic systems, which can model both retarded and neutral type systems, might be sensitive with respect to arbitrarily small delay perturbations. This recently led to the concept of strong H-infinity norms, which explicitly take into account such small delay perturbations. We present a direct numerical method to compute the strong H-infinity norm of SISO time-delay systems. Our algorithm is applicable to the closed-loop system of interconnections (series, parallel, feedback, junctions) of time-delay systems and/or controllers.
