scholarly journals Uniform stability and uniform asymptotic stability of sets with respect to a continuous flow

1972 ◽  
Vol 097 (1) ◽  
pp. 86-93
Author(s):  
František Tumajer
Keyword(s):  
Asymptotic Stability ◽  
Continuous Flow ◽  
Uniform Stability ◽  
Uniform Asymptotic Stability

scholarly journals On the Uniform Stability of Impulsive Lotka-Volterra Type Systems with Supremums

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Type Systems ◽  
Uniform Stability ◽  
Volterra Model ◽  
Uniform Asymptotic Stability ◽  
Volterra Type

In this paper we propose an impulsive n- species Lotka-Volterra model with supremums. By using Lyapunov method we give sufficient conditions for uniform stability and uniform asymptotic stability of the positive states.

Asymptotic Stability for an Impulsive Model of Hematopoiesis with Time Delay

2012 ◽  
Vol 204-208 ◽  
pp. 4506-4512
Author(s):  
Rui Chen ◽  
Pei Jun Ju
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Function Method ◽  
Uniform Stability ◽  
Uniform Asymptotic Stability ◽  
Lyapunov Function Method ◽  
Impulsive Model

A model of hematopoiesis with time delay and impulses is studied. Based on the Lyapunov function method, uniform stability and uniform asymptotic stability of the equilibria is discussed.

scholarly journals Review of Some Control Theory Results on Uniform Stability of Impulsive Systems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1186 ◽  
Author(s):  
Bin Liu ◽  
Bo Xu ◽  
Guohua Zhang ◽  
Lisheng Tong
Keyword(s):  
Asymptotic Stability ◽  
Control Theory ◽  
Hybrid Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Uniform Stability ◽  
Impulsive Systems ◽  
Uniform Asymptotic Stability ◽  
Stability Results ◽  
Stability Concepts

This paper aims to review some uniform stability results for impulsive systems. For the review, we classify the models of impulsive systems into time-based impulsive systems and state-based ones, including continuous-time impulsive systems, discrete-time impulsive systems, stochastic impulsive systems, and impulsive hybrid systems. According to these models, we review, respectively, the related stability concepts and some representative results focused on uniform stability, including the results on uniform asymptotic stability, input-to-state stability (ISS), KLL -stability (uniform stability expressed by KLL -functions), event-stability, and event-ISS. And we formulate some questions for those not fully developed aspects on uniform stability at each subsection.

On Problem of Partial Stability for Functional Differential Systems with Holdover

2019 ◽  
Vol 20 (7) ◽  
pp. 398-404
Author(s):  
V. I. Vorotnikov
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Position ◽  
Functional Differential Equations ◽  
Uniform Stability ◽  
Uniform Asymptotic Stability ◽  
Partial Stability ◽  
Additional Group ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Zero Equilibrium

The theory of systems of functional differential equations is a significant and rapidly developing sphere of modern mathematics which finds extensive application in complex systems of automatic control and also in economic, modern technical, ecological, and biological models. Naturally, the problems arises of stability and partial stability of the processes described by the class of the equation. The article studies the problem of partial stability which arise in applications either from the requirement of proper performance of a system or in assessing system capability. Also very effective is the approach to the problem of stability with respect to all variables based on preliminary analysis of partial stability. We suppose that the system have the zero equilibrium position. A conditions are obtained under which the uniform stability (uniform asymptotic stability) of the zero equilibrium position with respect to the part of the variables implies the uniform stability (uniform asymptotic stability) of this equilibrium position with respect to the other, larger part of the variables, which include an additional group of coordinates of the phase vector. These conditions include: 1) the condition for uniform asymptotic stability of the zero equilibrium position of the "reduced" subsystem of the original system with respect to the additional group of variables; 2) the restriction on the coupling between the "reduced" subsystem and the rest parts of the system. Application of the obtained results to a problem of stabilization with respect to a part of the variables for nonlinear controlled systems is discussed.

scholarly journals On the Stability of Some Discrete Fractional Nonautonomous Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Kübra Biçen
Keyword(s):  
Asymptotic Stability ◽  
Global Stability ◽  
Direct Method ◽  
Uniform Stability ◽  
Lyapunov Direct Method ◽  
Uniform Asymptotic Stability ◽  
Fractional Difference ◽  
Nonautonomous Systems ◽  
The Stability

Using the Lyapunov direct method, the stability of discrete nonautonomous systems within the frame of the Caputo fractional difference is studied. The conditions for uniform stability, uniform asymptotic stability, and uniform global stability are discussed.

scholarly journals On a problem of Hahn

1976 ◽  
Vol 14 (3) ◽  
pp. 321-324
Author(s):  
W.A. Coppel
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Uniform Stability ◽  
Linear Differential System ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability ◽  
Periodic Linear ◽  
Linear Differential

It is shown that for any almost periodic linear differential system asymptotic stability and uniform stability together imply uniform asymptotic stability.

scholarly journals Stability of Volterra system with impulsive effect

1991 ◽  
Vol 4 (1) ◽  
pp. 83-93 ◽  
Author(s):  
M. Ramamohana Rao ◽  
S. Sivasundaram
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Uniform Stability ◽  
Impulsive Effect ◽  
Property A ◽  
Uniform Asymptotic Stability ◽  
Volterra System ◽  
Piecewise Continuous ◽  
The Given

Sufficient conditions for uniform stability and uniform asymptotic stability of impulsive integrodifferential equations are investigated by constructing a suitable piecewise continuous Lyapunov-like functionals without the decresent property. A result which establishes no pulse phenomena in the given system is also discussed.

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