2,956 research outputs found
On the mixed sensitivity minimization for systems with infinitely many unstable modes
In this note we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers and a data transformation, we show that ℋ ∞ controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes. © 2004 Elsevier B.V. All rights reserved
Lectures on the functional renormalization group method
These introductory notes are about functional renormalization group equations
and some of their applications. It is emphasised that the applicability of this
method extends well beyond critical systems, it actually provides us a general
purpose algorithm to solve strongly coupled quantum field theories. The
renormalization group equation of F. Wegner and A. Houghton is shown to resum
the loop-expansion. Another version, due to J. Polchinski, is obtained by the
method of collective coordinates and can be used for the resummation of the
perturbation series. The genuinely non-perturbative evolution equation is
obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants
of this scheme are presented where the scale which determines the order of the
successive elimination of the modes is extracted from external and internal
spaces. The renormalization of composite operators is discussed briefly as an
alternative way to arrive at the renormalization group equation. The scaling
laws and fixed points are considered from local and global points of view.
Instability induced renormalization and new scaling laws are shown to occur in
the symmetry broken phase of the scalar theory. The flattening of the effective
potential of a compact variable is demonstrated in case of the sine-Gordon
model. Finally, a manifestly gauge invariant evolution equation is given for
QED.Comment: 47 pages, 11 figures, final versio
Sensitivity reduction by stable controllers for MIMO infinite dimensional systems via the tangential nevanlinna-pick interpolation
Cataloged from PDF version of article.We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in (C) over bar (+), but they are allowed to possess infinitely many poles in C+. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method
Stable H∞ controller design for time-delay systems
This paper investigates stable suboptimal [image omitted] controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the central suboptimal controller) may be unstable with finitely or infinitely many poles in +. For each of these cases, search algorithms are proposed to find stable suboptimal [image omitted] controllers. These design methods are illustrated with examples
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