12,732 research outputs found
Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
Several recent methods used to analyze asymptotic stability of
delay-differential equations (DDEs) involve determining the eigenvalues of a
matrix, a matrix pencil or a matrix polynomial constructed by Kronecker
products. Despite some similarities between the different types of these
so-called matrix pencil methods, the general ideas used as well as the proofs
differ considerably. Moreover, the available theory hardly reveals the
relations between the different methods.
In this work, a different derivation of various matrix pencil methods is
presented using a unifying framework of a new type of eigenvalue problem: the
polynomial two-parameter eigenvalue problem, of which the quadratic
two-parameter eigenvalue problem is a special case. This framework makes it
possible to establish relations between various seemingly different methods and
provides further insight in the theory of matrix pencil methods.
We also recognize a few new matrix pencil variants to determine DDE
stability.
Finally, the recognition of the new types of eigenvalue problem opens a door
to efficient computation of DDE stability
Quantum phase estimation algorithms with delays: effects of dynamical phases
The unavoidable finite time intervals between the sequential operations
needed for performing practical quantum computing can degrade the performance
of quantum computers. During these delays, unwanted relative dynamical phases
are produced due to the free evolution of the superposition wave-function of
the qubits. In general, these coherent "errors" modify the desired quantum
interferences and thus spoil the correct results, compared to the ideal
standard quantum computing that does not consider the effects of delays between
successive unitary operations. Here, we show that, in the framework of the
quantum phase estimation algorithm, these coherent phase "errors", produced by
the time delays between sequential operations, can be avoided by setting up the
delay times to satisfy certain matching conditions.Comment: 10 pages, no figur
An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
In this work, we revisit a criterion, originally proposed in [Nonlinearity
{\bf 17}, 207 (2004)], for the stability of solitary traveling waves in
Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the
implications of this criterion from the point of view of stability theory, both
at the level of the spectral analysis of the advance-delay differential
equations in the co-traveling frame, as well as at that of the Floquet problem
arising when considering the traveling wave as a periodic orbit modulo a shift.
We establish the correspondence of these perspectives for the pertinent
eigenvalue and Floquet multiplier and provide explicit expressions for their
dependence on the velocity of the traveling wave in the vicinity of the
critical point. Numerical results are used to corroborate the relevant
predictions in two different models, where the stability may change twice. Some
extensions, generalizations and future directions of this investigation are
also discussed
Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using The Matrix Lambert W function
This paper revisits a recently developed methodology based on the matrix
Lambert W function for the stability analysis of linear time invariant, time
delay systems. By studying a particular, yet common, second order system, we
show that in general there is no one to one correspondence between the branches
of the matrix Lambert W function and the characteristic roots of the system.
Furthermore, it is shown that under mild conditions only two branches suffice
to find the complete spectrum of the system, and that the principal branch can
be used to find several roots, and not the dominant root only, as stated in
previous works. The results are first presented analytically, and then verified
by numerical experiments
Stability of solutions to nonlinear wave equations with switching time-delay
In this paper we study well-posedness and asymptotic stability for a class of
nonlinear second-order evolution equations with intermittent delay damping.
More precisely, a delay feedback and an undelayed one act alternately in time.
We show that, under suitable conditions on the feedback operators, asymptotic
stability results are available. Concrete examples included in our setting are
illustrated. We give also stability results for an abstract model with
alternate positive-negative damping, without delay
Control of MTDC Transmission Systems under Local Information
High-voltage direct current (HVDC) is a commonly used technology for
long-distance electric power transmission, mainly due to its low resistive
losses. In this paper a distributed controller for multi-terminal high-voltage
direct current (MTDC) transmission systems is considered. Sufficient conditions
for when the proposed controller renders the closed-loop system asymptotically
stable are provided. Provided that the closed loop system is asymptotically
stable, it is shown that in steady-state a weighted average of the deviations
from the nominal voltages is zero. Furthermore, a quadratic cost of the current
injections is minimized asymptotically
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