The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Qing Hui - One of the best experts on this subject based on the ideXlab platform.
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Semistability of retarded functional differential Equations
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Qing HuiAbstract:In this paper, we develop a semistability analysis framework for retarded functional differential Equations (RFDE) having a continuum of equilibria with time-varying parameters and delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown heterogeneous time-varying delays and parameters along the communication links. We show that for such a retarded functional differential Equation, if the system asymptotically converges to an autonomous functional differential inclusion with constant time-delays and this new system is semistable, then the original retarded functional differential Equation system is semistable, provided that the delays are just bounded, not necessarily differentiable. In proving our results, we extend the limiting Equation approach to the retarded functional differential Equation systems and also develop some new convergence results for functional differential Equations and differential inclusions.
Mahmoud A Zaky - One of the best experts on this subject based on the ideXlab platform.
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numerical algorithm for the variable order caputo fractional functional differential Equation
Nonlinear Dynamics, 2016Co-Authors: Ali H. Bhrawy, Mahmoud A ZakyAbstract:While several high-order methods have been extensively developed for fixed-order fractional differential Equations (FDEs), there are no such methods for variable-order FDEs. In this paper, we propose an accurate and robust approach to approximate the solution of functional Dirichlet boundary value problem with a type of variable-order Caputo fractional derivative. The proposed method is principally based on the shifted Chebyshev polynomials as basis functions and the matrix representation of variable-order fractional derivative of such polynomials. The underline variable-order FDE is then reduced to a system of algebraic Equations, which greatly simplifies the solution process. Through numerical results, we confirm that the proposed scheme is very efficient and accurate for handling such problem.
John A. D. Appleby - One of the best experts on this subject based on the ideXlab platform.
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Subexponential growth rates in functional differential Equations
Dynamical Systems and Differential Equations AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid Spain), 2015Co-Authors: John A. D. Appleby, Denis D. PattersonAbstract:This paper determines the rate of growth to infinity of a scalar autonomous nonlinear functional differential Equation with finite delay, where the right hand side is a positive continuous linear functional of $f(x)$. We assume $f$ grows sublinearly, and is such that solutions should exhibit growth faster than polynomial, but slower than exponential. Under some technical conditions on $f$, it is shown that the solution of the functional differential Equation is asymptotic to that of an auxiliary autonomous ordinary differential Equation with righthand side proportional to $f$ (with the constant of proportionality equal to the mass of the finite measure associated with the linear functional), provided $f$ grows more slowly than $l(x)=x/\log x$. This linear--logarithmic growth rate is also shown to be critical: if $f$ grows more rapidly than $l$, the ODE dominates the FDE; if $f$ is asymptotic to a constant multiple of $l$, the FDE and ODE grow at the same rate, modulo a constant non--unit factor.
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Stochastic stabilisation of functional differential Equations
Systems & Control Letters, 2005Co-Authors: John A. D. Appleby, Xuerong MaoAbstract:In this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential Equation. Given an unstable functional differential Equation dx(t)/dt=f(t,xt), we stochastically perturb it into a stochastic functional differential Equation dX(t)=f(t,Xt)dt+ΣX(t)dB(t), where Σ is a matrix and B(t) a Brownian motion while Xt={X(t+θ):-τ⩽θ⩽0}. Under the condition that f satisfies the local Lipschitz condition and obeys the one-side linear bound, we show that if the time lag τ is sufficiently small, there are many matrices Σ for which the stochastic functional differential Equation is almost surely exponentially stable while the corresponding functional differential Equation dx(t)/dt=f(t,xt) may be unstable.
Ali H. Bhrawy - One of the best experts on this subject based on the ideXlab platform.
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numerical algorithm for the variable order caputo fractional functional differential Equation
Nonlinear Dynamics, 2016Co-Authors: Ali H. Bhrawy, Mahmoud A ZakyAbstract:While several high-order methods have been extensively developed for fixed-order fractional differential Equations (FDEs), there are no such methods for variable-order FDEs. In this paper, we propose an accurate and robust approach to approximate the solution of functional Dirichlet boundary value problem with a type of variable-order Caputo fractional derivative. The proposed method is principally based on the shifted Chebyshev polynomials as basis functions and the matrix representation of variable-order fractional derivative of such polynomials. The underline variable-order FDE is then reduced to a system of algebraic Equations, which greatly simplifies the solution process. Through numerical results, we confirm that the proposed scheme is very efficient and accurate for handling such problem.
M. Sjoerd - One of the best experts on this subject based on the ideXlab platform.
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Identification problems in functional differential Equations
Proceedings of the 36th IEEE Conference on Decision and Control, 1Co-Authors: V. Lunel, M. SjoerdAbstract:We outline how operator theory can be exploited to solve the problem of unique identification of coefficient matrices, time delays and initial functions of a linear retarded functional differential Equation.
