TL;DR: In this article, Bode's concepts of return difference and return ratio are shown to play a fundamental role in the analysis of multivariable feedback control systems, and the corresponding characteristic frequency responses provide a simple and natural link between classical single-loop design techniques and multi-ivariable-system feedback theory.
Abstract: Bode's concepts of return difference and return ratio are shown to play a fundamental role in the analysis of multivariable feedback control systems. Matrix transfer functions are regarded as operators on linear vector spaces over the field of rational functions in the complex variable s. The eigenvalues of such operators are identified as characteristic transfer functions. The corresponding characteristic frequency responses provide a simple and natural link between classical single-loop design techniques and multivariable-system feedback theory. These concepts then serve as a unifying thread in a coherent and systematic discussion of multivariable-feedback-system design techniques.
TL;DR: The RA-AGAT architecture is capable of surpassing the previously applicable methods in the prediction and recommendation of stock return ratio and verified the practicality and applicability of the application of graph models in finance.
TL;DR: The loop-based two-port algorithm and device-based gain-nulling are proposed for small-signal stability analysis, which determines the stability of a feedback network in which a controlled source can be nulled to render the network to be passive.
Abstract: In this article, based on Bode's definition of return ratio with respect to a single controlled source, the loop-based two-port algorithm and device-based gain-nulling are proposed for small-signal stability analysis. These two algorithms are complementary in terms of applicability, and they produce accurate stability information for single-loop networks. After a brief primer on feedback and stability, we review Bode's feedback theory, where the return difference and return ratio concepts are applicable to general feedback configurations and avoid the necessity of identifying /spl mu/ and /spl beta/. Middlebrook's null double-injection technique, which provides a laboratory-based way to measure return ratio, is then discussed in the modern circuit analysis context; we then extend the unilateral feedback-model used in Middlebrook's approach to accommodate both normal-and reverse-loop transmission and characterize the return loop using a general two-port-analysis. This loop-based two-port algorithm determines the stability of a feedback network in which a critical wire can be located to break all return loops. The device-based gain-nulling algorithm is then discussed to evaluate the influence of the local return loops upon network stability. This algorithm determines the stability of a feedback network in which a controlled source can be nulled to render the network to be passive. Conditions under which these two algorithms can be applied are discussed.
TL;DR: Two approaches for analyzing single-loop feedback circuits are compared and contrasted and a frequent error in many popular texts-interchanging the computation of return ratio for a dependent source and loop gain of the idealized feedback network-is discussed.
Abstract: Two approaches for analyzing single-loop feedback circuits are compared and contrasted. One approach is based on the return-radio concept, and the other is based on two-port analysis. A frequent error in many popular texts-interchanging the computation of return ratio for a dependent source and loop gain of the idealized feedback network-is discussed. Assumptions commonly made in many texts when presenting two-port feedback analysis are examined for validity. Examples are given to highlight the differences between the two approaches. >
TL;DR: The robust optimization models for two variants of stable tail-adjusted return ratio, one with mixed conditional value-at-risk (MCVaR) and the other with deviation MCVaR, under joint ambiguity in the distribution modeled using copulas are introduced.