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 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.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

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.

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 Stability and boundedness to certain differential equations of fourth order with multiple delays

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1049-1058 ◽  
Author(s):  
Erdal Korkmaz ◽  
Cemil Tunc
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Multiple Delays ◽  
Boundedness Of Solutions ◽  
Functional Differential ◽  
The Stability

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple delays. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

scholarly journals Asymptotic stability of the time-changed stochastic delay differential equations with Markovian switching

2021 ◽  
Vol 19 (1) ◽  
pp. 614-628
Author(s):  
Xiaozhi Zhang ◽  
Zhangsheng Zhu ◽  
Chenggui Yuan
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Stability Of Solutions ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
The Stability ◽  
Delay Differential

Abstract The aim of this work is to study the asymptotic stability of the time-changed stochastic delay differential equations (SDDEs) with Markovian switching. Some sufficient conditions for the asymptotic stability of solutions to the time-changed SDDEs are presented. In contrast to the asymptotic stability in existing articles, we present the new results on the stability of solutions to time-changed SDDEs, which is driven by time-changed Brownian motion. Finally, an example is given to demonstrate the effectiveness of the main results.

scholarly journals Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
Functional Differential ◽  
The Stability

AbstractWe consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.

ON THE STABILITY OF SOLUTIONS OF NONLINEAR SYSTEMS WITH IMPULSE STRUCTURE

2018 ◽  
pp. 624-636
Author(s):  
Natalia Igorevna Zhelonkina ◽  
Alexander Nikolaevich Sesekin
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Stability Property ◽  
Sufficient Conditions ◽  
Functions Of Bounded Variation ◽  
Stability Of Solutions ◽  
Smooth Solutions ◽  
Systems Of Differential Equations ◽  
The Stability ◽  
The Right

In this paper we review the results of the authors related to the study of the stability property of solutions for nonlinear systems of differential equations, on the right-hand side of which there are terms containing products of discontinuous functions and distributions. The solutions of such systems are formalized by the closure of the set of smooth solutions in the space of functions of bounded variation. For such systems, sufficient conditions are obtained for the asymptotic stability of unperturbed solutions.

Stability analysis of differential equations with maximum

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Uniform Stability

AbstractIn this paper, we investigate stability of the zero solution of differential equations with maximum by using Lyapunov functions and Razumikhin techniques. Sufficient conditions for stability, uniform stability and asymptotic stability of the zero solution of such equations are found.

scholarly journals Stability in higher-order nonlinear fractional differential equations

2018 ◽  
Vol 22 (1) ◽  
pp. 37-47
Author(s):  
Abdelouaheb Ardjouni ◽  
Hamid Boulares ◽  
Yamina Laskri
Keyword(s):  
Banach Space ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Higher Order ◽  
Nonlinear Fractional Differential Equations ◽  
Weighted Banach Space ◽  
Fractional Differential

We give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of higher-order nonlinear fractional differential equations. By using Krasnoselskii's xed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that f (t, 0) = 0. The results obtained here generalize the work of Ge and Kou.

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