Further results on the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays (original) (raw)
Related papers
Asymptotic stability of nonlinear perturbed neutral linear fractional system with distributed delay
THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020), 2021
In the present paper we study the stability properties of nonlinear perturbed neutral fractional autonomous linear differential systems with distributed delay. It is shown that if the zero solution of the linear part of the nonlinear perturbed system is globally asymptotically stable, then the zero solution of the perturbed nonlinear system is globally asymptotically stable too. The results are based on a formula for the integral presentation of the general solution of a linear autonomous neutral system with distributed delay which was proved by the authors in a previous work.
Stabilization of some fractional delay systems of neutral type
Automatica, 2007
In this note, we give new stability tests which enable one to fully characterize the H ∞-stability of systems with transfer function G(s) = r(s) p(s)+q(s) e −sh , where h > 0 and p, q, r are real polynomials in the variable s for 0 < < 1. As an application of this, in the case r(s) = 1 and deg p = deg q = 1, families of H ∞-stabilizing controllers are given and a complete parametrization of all H ∞-stabilizing controllers is obtained when |lim s∈C\R − |s|→∞ p(s)/q(s)| > 1.
Mathematics
In the present paper, sufficient conditions are obtained under which the Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has a unique solution in the case of initial functions with first-kind discontinuities. For this system, by applying a formula for the integral presentation of the solution of the nonhomogeneous linear neutral fractional system, we found some additional natural conditions to ensure that from the global asymptotically stability of the zero solution of the linear part of the nonlinearly perturbed system, global asymptotic stability of the zero solution of the whole nonlinearly perturbed system follows.
$H_\infty$-Stability Analysis of Fractional Delay Systems of Neutral Type
SIAM Journal on Control and Optimization, 2016
In this paper we consider linear fractional systems of commensurate orders and with commensurate delays, whose characteristic equation is a polynomial in the two variables s α (0 < α < 1) and e −sτ (τ > 0). These systems may have single or multiple chains of poles asymptotic to the imaginary axis. Location of poles of large modulus belonging to these chains are determined by approximation and simple necessary and sufficient H∞-stability conditions are derived.
On the Asymptotic Stability of a Nonlinear Fractional-order System with Multiple Variable Delays
2020
In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink
Journal of Mathematics
In this paper, the asymptotic stability of solutions is investigated for a class of nonlinear fractional neutral neural networks with time-dependent delays which are unbounded. By constructing the appropriate Lyapunov functional, sufficient conditions for asymptotic stability of neural networks are obtained with the help of LMI. An example is presented by using the LMI Toolbox to demonstrate the effectiveness of the obtained results.
This paper is concerned with the asymptotic stability of linear fractional-order neutral delay differential-algebraic systems described by the Caputo-Fabrizio (CF) fractional derivative. A novel characteristic equation is derived using the Laplace transform. Based on an algebraic approach, stability criteria are established. The effect of the index on such criteria is analyzed to ensure the asymptotic stability of the system. It is shown that asymptotic stability is ensured for the index-1 problems provided that a stability criterion holds for any delay parameter. Also, asymptotic stability is still valid for higher-index problems under the conditions that the system matrices have common eigenvectors and each pair of such matrices is simultaneously triangularizable so that a stability criterion holds for any delay parameter. An example is provided to demonstrate the effectiveness and applicability of the theoretical results.
Journal of Computational and Applied Mathematics, 2012
In this paper, several analytical and numerical approaches are presented for the stability analysis of linear fractional-order delay differential equations. The main focus of interest is asymptotic stability, but bounded-input bounded-output (BIBO) stability is also discussed. The applicability of the Laplace transform method for stability analysis is first investigated, jointly with the corresponding characteristic equation, which is broadly used in BIBO stability analysis. Moreover, it is shown that a different characteristic equation, involving the one-parameter Mittag-Leffler function, may be obtained using the well-known method of steps, which provides a necessary condition for asymptotic stability. Stability criteria based on the Argument Principle are also obtained. The stability regions obtained using the two methods are evaluated numerically and comparison results are presented. Several key problems are highlighted.