Structure and Output Feedback in Singular Systems

形式为Ex= Ax + Bu的广义状态空间系统，E通常为单数，在机器人、网络、大规模互联系统、电力系统、经济系统、延迟微分系统、神经网络和其他领域的研究中自然出现。我们的主要论点是，状态变量理论有一些严重的局限性，而奇异系统提供了一个更一般的背景，可以对状态变量系统的一些深层次问题产生重要的见解。两个重要的案例将研究在拟议的研究。首先，我们指出状态空间系统的逆不是状态变量系统。实际上，逆通常包含输出的导数，因此它是一个奇异系统。因此，奇异系统，而不是状态变量系统，为研究与反演有关的问题提供了自然的动力学公式。这包括高粒度反馈、奇异最优控制（传统意义上的不完全控制权重）和其他重要问题以及通常的系统反演问题。因此，我们的第一个目标是研究奇异系统结构算法的扩展和性质，该算法已经发展到与奇异系统的反演和最优控制有关。其次，如果将比例加导数输出反馈应用于状态空间系统，则结果是奇异系统而不是状态变量系统。因此，这些系统为实现我们的第二个目标提供了一个自然的公式，即研究状态变量和奇异系统中的比例+导数输出反馈。最近的结果清楚地表明，使用这种技术，可以实现比传统的最小（n, m+p-1）极点分配更多。

Generalized state-space systems of the form Ex= Ax + Bu, with E generally singular, arise naturally in the study of robots, networks, large-scale interconnected systems, power systems, economic systems, delay-differential systems, neural networks, and elsewhere. Our main contentions are that there are some serious limitations in state-variable theory and that singular systems provide a more general context that yields important insight into some deep questions about state-variable systems. Two important cases will be studied in the proposed research. First, we point out that the inverse of a state-space system is not a state-variable system. Indeed, the inverse generally contains derivatives of the output, so that it is a singular system. Therefore, singular systems, not state-variable systems, provide the natural dynamical formulation for the study of issues related to inversion. This includes high-grain feedback, singular optimal control (in the traditional sense of incomplete control weighting), and other important problems as well as the usual system inversion problems. Our first goal is, therefore, to study the extensions and properties of the Singular System Structure Algorithm which has been developed in connection with inversion and optimal control of singular systems. Second, if proportional-plus-derivative output feedback is applied to a state-space system, the result is a singular and not a state- variable system. These systems therefore provide a nature formulation for carrying out our second goal, the study of proportional-plus derivative output feedback in state-variable and singular systems. Recent results make it clear that using this technique, far more can be achieved than the assignment of the traditional min(n, m+p-1) poles.