6,028 research outputs found
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures
A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances
The official published version of this article can be found at the link below.This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60774073 and 60974030, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany
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
Turing's model for biological pattern formation and the robustness problem
One of the fundamental questions in developmental biology is how the vast range of pattern and structure we observe in nature emerges from an almost uniformly homogeneous fertilized egg. In particular, the mechanisms by which biological systems maintain robustness, despite being subject to numerous sources of noise, are shrouded in mystery. Postulating plausible theoretical models of biological heterogeneity is not only difficult, but it is also further complicated by the problem of generating robustness, i.e. once we can generate a pattern, how do we ensure that this pattern is consistently reproducible in the face of perturbations to the domain, reaction time scale, boundary conditions and so forth. In this paper, not only do we review the basic properties of Turing's theory, we highlight the successes and pitfalls of using it as a model for biological systems, and discuss emerging developments in the area
Relative controllability of linear difference equations
In this paper, we study the relative controllability of linear difference
equations with multiple delays in the state by using a suitable formula for the
solutions of such systems in terms of their initial conditions, their control
inputs, and some matrix-valued coefficients obtained recursively from the
matrices defining the system. Thanks to such formula, we characterize relative
controllability in time in terms of an algebraic property of the
matrix-valued coefficients, which reduces to the usual Kalman controllability
criterion in the case of a single delay. Relative controllability is studied
for solutions in the set of all functions and in the function spaces and
. We also compare the relative controllability of the system for
different delays in terms of their rational dependence structure, proving that
relative controllability for some delays implies relative controllability for
all delays that are "less rationally dependent" than the original ones, in a
sense that we make precise. Finally, we provide an upper bound on the minimal
controllability time for a system depending only on its dimension and on its
largest delay
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