17,686 research outputs found
Backward Linear Control Systems on Time Scales
We show how a linear control systems theory for the backward nabla
differential operator on an arbitrary time scale can be obtained via Caputo's
duality. More precisely, we consider linear control systems with outputs
defined with respect to the backward jump operator. Kalman criteria of
controllability and observability, as well as realizability conditions, are
proved.Comment: Submitted November 11, 2009; Revised March 28, 2010; Accepted April
03, 2010; for publication in the International Journal of Control
Realization Theory for LPV State-Space Representations with Affine Dependence
In this paper we present a Kalman-style realization theory for linear
parameter-varying state-space representations whose matrices depend on the
scheduling variables in an affine way (abbreviated as LPV-SSA representations).
We deal both with the discrete-time and the continuous-time cases. We show that
such a LPV-SSA representation is a minimal (in the sense of having the least
number of state-variables) representation of its input-output function, if and
only if it is observable and span-reachable. We show that any two minimal
LPV-SSA representations of the same input-output function are related by a
linear isomorphism, and the isomorphism does not depend on the scheduling
variable.We show that an input-output function can be represented by a LPV-SSA
representation if and only if the Hankel-matrix of the input-output function
has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension
of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart
of partial realization theory for LPV-SSA representation and prove correctness
of the Kalman-Ho algorithm. These results thus represent the basis of systems
theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as
follows: typos have been fixe
Enhanced LFR-toolbox for MATLAB and LFT-based gain scheduling
We describe recent developments and enhancements of the LFR-Toolbox for MATLAB for building LFT-based uncertainty models and for LFT-based gain scheduling. A major development is the new LFT-object definition supporting a large class of uncertainty descriptions: continuous- and discrete-time uncertain models, regular and singular parametric expressions, more general uncertainty blocks (nonlinear, time-varying, etc.). By associating names to uncertainty blocks the reusability of generated LFT-models and the user friendliness of manipulation of LFR-descriptions have been highly increased. Significant enhancements of the computational efficiency and of numerical accuracy have been achieved by employing efficient and numerically robust Fortran implementations of order reduction tools via mex-function interfaces. The new enhancements in conjunction with improved symbolical preprocessing lead generally to a faster generation of LFT-models with significantly lower orders. Scheduled gains can be viewed as LFT-objects. Two techniques for designing such gains are presented. Analysis tools are also considered
Self-Dual N=2 Born-Infeld Theory Through Auxiliary Superfields
There is an evidence that the N=2 Born-Infeld theory with spontaneously
broken N=4 supersymmetry exhibits self-duality. We perform a further check of
this hypothesis by constructing a new representation for the N=2 Born-Infeld
action through the auxiliary chiral superfield U. In such a formulation,
self-duality is equivalent to U(1) invariance of the U interaction. We
explicitly calculate the auxiliary interaction up to the 10th order and show
its U(1) duality invariance, thus proving that the original action is self-dual
to the same order. We also suggest a new method of recursive computation of the
N=2 Born-Infeld action in the standard formulation, based solely on the
nonlinear realization of the N=4 central charge on the N=2 superfield strengths
W, \bar W.Comment: 1 + 31 pages, substantial revision: an important Note and Appendix C
added; section 2 corrected and expanded; some typos, eq. (5.13) and Appendix
B correcte
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
A general framework is presented for analyzing the stability and performance
of nonlinear and linear parameter varying (LPV) time delayed systems. First,
the input/output behavior of the time delay operator is bounded in the
frequency domain by integral quadratic constraints (IQCs). A constant delay is
a linear, time-invariant system and this leads to a simple, intuitive
interpretation for these frequency domain constraints. This simple
interpretation is used to derive new IQCs for both constant and varying delays.
Second, the performance of nonlinear and LPV delayed systems is bounded using
dissipation inequalities that incorporate IQCs. This step makes use of recent
results that show, under mild technical conditions, that an IQC has an
equivalent representation as a finite-horizon time-domain constraint. Numerical
examples are provided to demonstrate the effectiveness of the method for both
class of systems
Quantum state transfer in a q-deformed chain
We investigate the quantum state transfer in a chain of particles satisfying
q-deformed oscillators algebra. This general algebraic setting includes the
spin chain and the bosonic chain as limiting cases. We study conditions for
perfect state transfer depending on the number of sites and excitations on the
chain. They are formulated by means of irreducible representations of a quantum
algebra realized through Jordan-Schwinger maps. Playing with deformation
parameters, we can study the effects of nonlinear perturbations or interpolate
between the spin and bosonic chain.Comment: 13 pages, 4 figure
Phenomenological Quantum Gravity
These notes summarize a set of lectures on phenomenological quantum gravity
which one of us delivered and the other attended with great diligence. They
cover an assortment of topics on the border between theoretical quantum gravity
and observational anomalies. Specifically, we review non-linear relativity in
its relation to loop quantum gravity and high energy cosmic rays. Although we
follow a pedagogic approach we include an open section on unsolved problems,
presented as exercises for the student. We also review varying constant models:
the Brans-Dicke theory, the Bekenstein varying model, and several more
radical ideas. We show how they make contact with strange high-redshift data,
and perhaps other cosmological puzzles. We conclude with a few remaining
observational puzzles which have failed to make contact with quantum gravity,
but who knows... We would like to thank Mario Novello for organizing an
excellent school in Mangaratiba, in direct competition with a very fine beach
indeed.Comment: Lectures given at XI BSC
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