5,859 research outputs found
Stability and performance analysis of linear positive systems with delays using input-output methods
It is known that input-output approaches based on scaled small-gain theorems
with constant -scalings and integral linear constraints are non-conservative
for the analysis of some classes of linear positive systems interconnected with
uncertain linear operators. This dramatically contrasts with the case of
general linear systems with delays where input-output approaches provide, in
general, sufficient conditions only. Using these results we provide simple
alternative proofs for many of the existing results on the stability of linear
positive systems with discrete/distributed/neutral time-invariant/-varying
delays and linear difference equations. In particular, we give a simple proof
for the characterization of diagonal Riccati stability for systems with
discrete-delays and generalize this equation to other types of delay systems.
The fact that all those results can be reproved in a very simple way
demonstrates the importance and the efficiency of the input-output framework
for the analysis of linear positive systems. The approach is also used to
derive performance results evaluated in terms of the -, - and
-gains. It is also flexible enough to be used for design purposes.Comment: 34 page
Timing jitter of passively mode-locked semiconductor lasers subject to optical feedback; a semi-analytic approach
We propose a semi-analytical method of calculating the timing fluctuations in
mode-locked semiconductor lasers and apply it to study the effect of delayed
coherent optical feedback on pulse timing jitter in these lasers. The proposed
method greatly reduces computation times and therefore allows for the
investigation of the dependence of timing fluctuations over greater parameter
domains. We show that resonant feedback leads to a reduction in the timing
jitter and that a frequency-pulling region forms about the main resonances,
within which a timing jitter reduction is observed. The width of these
frequency-pulling regions increases linearly with short feedback delay times.
We derive an analytic expression for the timing jitter, which predicts a
monotonous decrease in the timing jitter for resonant feedback of increasing
delay lengths, when timing jitter effects are fully separated from amplitude
jitter effects. For long feedback cavities the decrease in timing jitter scales
approximately as with the increase of the feedback delay time
Robust passivity and passification of stochastic fuzzy time-delay systems
The official published version can be obtained from the link below.In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.This work was supported by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers 200802861044, the National Natural Science Foundation of China under Grant 60804028 and the Royal Society of the United Kingdom
Stability and stabilization of fractional order time delay systems
U ovom radu predstavljeni su neki osnovni rezultati koji se odnose na kriterijume stabilnosti sistema necelobrojnog reda sa kašnjenjem kao i za sisteme necelobrojnog reda bez kašnjenja.Takođe, dobijeni su i predstavljeni dovoljni uslovi za konačnom vremenskom stabilnost i stabilizacija za (ne)linearne (ne)homogene kao i za perturbovane sisteme necelobrojnog reda sa vremenskim kašnjenjem. Nekoliko kriterijuma stabilnosti za ovu klasu sistema necelobrojnog reda je predloženo korišćenjem nedavno dobijene generalizovane Gronval nejednakosti, kao i 'klasične' Belman-Gronval nejednakosti. Neki zaključci koji se odnose na stabilnost sistema necelobrojnog reda su slični onima koji se odnose na klasične sisteme celobrojnog reda. Na kraju, numerički primer je dat u cilju ilustracije značaja predloženog postupka.In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as 'classical' Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integerorder differential equations. Finally, a numerical example is given to illustrate the validity of the proposed procedure
Approximate and exact controllability of linear difference equations
In this paper, we study approximate and exact controllability of the linear
difference equation in
, with and , using as a basic
tool a representation formula for its solution in terms of the initial
condition, the control , and some suitable matrix coefficients. When
are commensurable, approximate and exact
controllability are equivalent and can be characterized by a Kalman criterion.
This paper focuses on providing characterizations of approximate and exact
controllability without the commensurability assumption. In the case of
two-dimensional systems with two delays, we obtain an explicit characterization
of approximate and exact controllability in terms of the parameters of the
problem. In the general setting, we prove that approximate controllability from
zero to constant states is equivalent to approximate controllability in .
The corresponding result for exact controllability is true at least for
two-dimensional systems with two delays
Time-delayed feedback control of shear-driven micellar systems
Suspensions of elongated micelles under shear display complex non-linear
behaviour including shear banding, spatio-temporal oscillatory patterns and
chaotic response. Based on a suitable rheological model [S. M. Fielding and P.
D. Olmsted, Phys. Rev. Lett. 92, 084502 (2004)], we here explore possibilities
to manipulate the dynamical behaviour via closed-loop (feedback) control
involving a time delay . The model considered relates the viscoelastic
stress of the system to a structural variable, that is, the length of the
micelles, yielding two time- and space-dependent dynamical variables ,
. As a starting point we perform a systematic linear stability analysis
of the uncontrolled system for (i) an externally imposed average shear rate and
(ii) an imposed total stress, and compare the results to those from extensive
numerical simulations. We then apply the so-called Pyragas feedback scheme
where the equations of motion are supplemented by a control term of the form
with being a measurable quantity depending
on the rheological protocol. For the choice of an imposed shear rate, the
Pyragas scheme for the total stress reduces to a non-diagonal scheme
concentrating on the viscoelastic stress. Focusing on parameters close to a
Hopf bifurcation, where the uncontrolled system displays oscillatory states as
well as hysteresis in the shear rate controlled protocol, we demonstrate that
(local) Pyragas control leads to a full stabilization to the steady state
solution of the total stress, while a global control scheme does not work. In
contrast, for the case of imposed total stress, global Pyragas control fully
stabilizes the system. In both cases, the control does not change the space of
solutions, rather it selects the steady state solutions out of the existing
solutions. This underlines the non-invasive character of the Pyragas scheme
Quantum feedback: theory, experiments, and applications
The control of individual quantum systems is now a reality in a variety of
physical settings. Feedback control is an important class of control methods
because of its ability to reduce the effects of noise. In this review we give
an introductory overview of the various ways in which feedback may be
implemented in quantum systems, the theoretical methods that are currently used
to treat it, the experiments in which it has been demonstrated to-date, and its
applications. In the last few years there has been rapid experimental progress
in the ability to realize quantum measurement and control of mesoscopic
systems. We expect that the next few years will see further rapid advances in
the precision and sophistication of feedback control protocols realized in the
laboratory.Comment: Updated version of a review paper about quantum feedbac
Chaos in time delay systems, an educational review
The time needed to exchange information in the physical world induces a delay
term when the respective system is modeled by differential equations. Time
delays are hence ubiquitous, being furthermore likely to induce instabilities
and with it various kinds of chaotic phases. Which are then the possible types
of time delays, induced chaotic states, and methods suitable to characterize
the resulting dynamics? This review presents an overview of the field that
includes an in-depth discussion of the most important results, of the standard
numerical approaches and of several novel tests for identifying chaos. Special
emphasis is placed on a structured representation that is straightforward to
follow. Several educational examples are included in addition as entry points
to the rapidly developing field of time delay systems
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