On Dynamic Feedback Compensation and Compactification of Systems
TLDR
In this article, a compactification of the space of proper transfer functions with a fixed McMillan degree was introduced, which has the structure of a projective variety and each point of this variety can be given an interpretation as a certain autoregressive system in the sense of Willems.Abstract:
This paper introduces a compactification of the space of proper $p\times m$ transfer functions with a fixed McMillan degree $n$. Algebraically, this compactification has the structure of a projective variety and each point of this variety can be given an interpretation as a certain autoregressive system in the sense of Willems. It is shown that the pole placement map with dynamic compensators turns out to be a central projection from this compactification to the space of closed-loop polynomials. Using this geometric point of view, necessary and sufficient conditions are given when a strictly proper or proper system can be generically pole assigned by a complex dynamic compensator of McMillan degree $q$.read more
Citations
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Introduction to numerical algebraic geometry
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A smooth compactification of the space of transfer functions with fixed McMillan degree
M.S. Ravi,Joachim Rosenthal +1 more
TL;DR: In this article, it is shown that the space of all proper or strictly proper p × m transfer functions of a fixed McMillan degreed has, in a natural way, the structure of a noncompact, smooth manifold.
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Output feedback pole placement with dynamic compensators
Joachim Rosenthal,Xiaochang Wang +1 more
TL;DR: The authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system by dynamic compensators of degree at most q.
References
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Linear systems
TL;DR: In this paper, the authors studied the effect of local derivatives on the detection of intensity edges in images, where the local difference of intensities is computed for each pixel in the image.
Journal ArticleDOI
Paradigms and puzzles in the theory of dynamical systems
TL;DR: In this article, a self-contained exposition is given of an approach to mathematical models, in particular to the theory of dynamical systems, which leads to a new view of the notions of controllability and observability, and of the interconnection of systems.
Journal ArticleDOI
Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
TL;DR: It is shown how minimal bases can be used to factor a transfer function matrix G in the form $G = ND^{ - 1} $, where N and D are polynomial matrices that display the controllability indices of G and its controller canonical realization.
Book
Algebraic Geometry I: Complex Projective Varieties
TL;DR: In the 20th century, algebraic geometry has gone through at least three distinct phases as mentioned in this paper, and the most important of them is the phase of the introduction of commutative algebra into algebraic geometrical geometry.
Journal ArticleDOI
Pole assignment by gain output feedback
TL;DR: In this article, it was shown that if the system is controllable and observable, and if n \leq r + m - 1, an almost arbitrary set of distinct closed-loop poles is assignable by gain output feedback, where n, r, and m are the numbers of state variables, inputs and outputs, respectively.