scholarly journals Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 390
Author(s):  
Andrey Zahariev ◽  
Hristo Kiskinov
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Global Asymptotic Stability ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Neutral System ◽  
Perturbed System ◽  
The Stability ◽  
Several Delays

In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.

scholarly journals On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type

2019 ◽  
pp. 161-166
Author(s):  
Natalia Sedova
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Auxiliary Function ◽  
Uniform Asymptotic Stability ◽  
Volterra Type ◽  
Razumikhin Technique ◽  
The Stability ◽  
The Right

The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 63
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Delayed Systems ◽  
Asymptotic Stabilization ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using inputoutput stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

scholarly journals THE GENERALISED LIÉNARD EQUATIONS

2009 ◽  
Vol 51 (3) ◽  
pp. 605-617
Author(s):  
A. AGHAJANI ◽  
A. MORADIFAM
Keyword(s):  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Oscillation Theory ◽  
Homoclinic Orbits ◽  
Liénard Equations ◽  
Existence Of Periodic Solutions ◽  
Image Position

AbstractIn this paper we present sufficient conditions for all trajectories of the system to cross the vertical isocline h(y) = F(x), which is very important in the global asymptotic stability of the origin, oscillation theory and existence of periodic solutions. Also we give sufficient conditions for all trajectories which start at a point on the curve h(y) = F(x), to cross the y-axis which is closely connected with the existence of homoclinic orbits, stability of the zero solution, oscillation theory and the centre problem. The obtained results extend and improve some of the authors' previous results and some other theorems in the literature.

scholarly journals On the stability of impulsively perturbed differential systems

1977 ◽  
Vol 17 (3) ◽  
pp. 423-432 ◽  
Author(s):  
S.G. Pandit
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Stability Property ◽  
Unperturbed System ◽  
Uniform Asymptotic Stability ◽  
Differential Systems ◽  
Perturbed System ◽  
Gronwall Integral Inequality ◽  
The Stability ◽  
Points Of Discontinuity

This paper deals with the study of uniform asymptotic stability of the measure differential system Dx = F(t, x) + G(t, x)Du, where the symbol D stands for the derivative in the sense of distributions. The system is viewed as a perturbed system of the ordinary differential system x' = F(t, x), where the perturbation term G(t, x)Du is impulsive and the state of the system changes suddenly at the points of discontinuity of u. It is shown, under certain conditions, that the uniform asymptotic stability property of the unperturbed system is shared by the perturbed system. To do this, the well-known Gronwall integral inequality is generalized so as to be applicable to Lebesgue-Stieltjes integrals.

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Input Output ◽  
Delayed Systems ◽  
Output Stability ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using input-output stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

Stability analysis of linear distributed order fractional systems with distributed delays

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Doychin Boyadzhiev ◽  
Hristo Kiskinov ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Density Function ◽  
Global Asymptotic Stability ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Distributed Delays ◽  
Fractional Systems ◽  
Distributed Order

AbstractIn the present work we study linear systems with distributed delays and distributed order fractional derivatives based on Caputo type single fractional derivatives, with respect to a nonnegative density function. For the initial problem of this kind of systems, existence, uniqueness and a priory estimate of the solution are proved. As an application of the obtained results, we establish sufficient conditions for global asymptotic stability of the zero solution of the investigated types of systems.

scholarly journals On Stability of Linear Delay Differential Equations under Perron's Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
J. Diblík ◽  
A. Zafer
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Uniform Asymptotic Stability ◽  
Linear Delay ◽  
Functional Differential ◽  
The Stability ◽  
Delay Differential

The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.

scholarly journals Stability of a Functional Differential System with a Finite Number of Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Stability Of Solutions ◽  
Functional Differential ◽  
The Stability ◽  
Complex Valued ◽  
Functional Differential System

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

Stability of Linear Systems With Multitask Right-Hand Member

2018 ◽  
pp. 74-112 ◽  
Author(s):  
G. V. Alferov ◽  
G. G. Ivanov ◽  
P. A. Efimova ◽  
A. S. Sharlay
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Computational Models ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Point Of View ◽  
Control Laws ◽  
Systems Of Differential Equations ◽  
The Stability

To study the dynamics of mechanical systems and to define the construction parameters and control laws, it is necessary to have computational models accurately describing properties of real mechanisms. From a mathematical point of view, the computational models of mechanical systems are actually the systems of differential equations. These models can contain equations that also describe non-mechanical phenomena. In this chapter, the problems of stability and asymptotic stability conditions for the motion of mechanical systems with holonomic and non-holonomic constraints are under consideration. Stability analysis for the systems of differential equations is given in term of the second Lyapunov's method. With the use of the set-theoretic approach, the necessary and sufficient conditions for stability and asymptotic stability of zero solution of the considered system are formulated. The proposed approaches can be used to study the stability of the motion for robot manipulators, transport, space, and socio-economic systems.

scholarly journals STABILITY OF ZERO SOLUTION OF SYSTEM WITH SWITCHES CONSISTING OF LINEAR SUBSYSTEMS

2020 ◽  
pp. 89-96
Author(s):  
D. Khusainov ◽  
A. Bychkov ◽  
A. Sirenko
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Switching Systems ◽  
Stability Of Solutions ◽  
Quadratic Lyapunov Function ◽  
Linear Differential ◽  
The Stability

In this paper, discusses the study of the stability of solutions of dynamic systems with switching. Sufficient conditions are obtained for the asymptotic stability of the zero solution of switching systems consisting of linear differential and difference subsystems. It is proved that the existence of a common quadratic Lyapunov function is sufficient for asymptotic stability.

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