# On the Partial Equiasymptotic Stability in Functional Differential Equations

@article{Ignatyev2002OnTP, title={On the Partial Equiasymptotic Stability in Functional Differential Equations}, author={Alexander O. Ignatyev}, journal={Journal of Mathematical Analysis and Applications}, year={2002}, volume={268}, pages={615-628} }

Abstract A system of functional differential equations with delay dz/dt = Z(t, zt), where Z is the vector-valued functional is considered. It is supposed that this system has a zero solution z = 0. Definitions of its partial stability, partial asymptotical stability, and partial equiasymptotical stability are given. Theorems on the partial equiasymptotical stability are formulated and proved.

## 34 Citations

### Partial equiasymptotic stability of nonlinear dynamic systems

- Mathematics
- 2005

For nonlinear nonautonomous dynamic systems, partial equiasymptotic stability of the zero equilibrium position, equiasymptotic stability of the “partial” equilibrium position, and partial…

### Partially equi-integral ϕ0-stability of nonlinear differential systems

- Mathematics
- 2016

This paper introduces the notions of partially equi-integral stability and partially equi-integral φ0-stability for two differential systems, and establishes some criteria on stability relative to…

### Stability results for systems described by retarded functional differential equations

- Mathematics2007 European Control Conference (ECC)
- 2007

In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations…

### PARTIAL STABILITY ANALYSIS BY MEANS OF SEMIDEFINITE LYAPUNOV FUNCTIONS

- Mathematics
- 2005

A nonautonomous system of ordinary differential equations is considered. This system has the zero solution, and there exists a nonnegative Lyapunov function which derivative is nonpositive. Theorems…

### Global Output Stability for Systems Described by Retarded Functional Differential Equations: Lyapunov Characterizations

- MathematicsEur. J. Control
- 2008

Characterizations of internal notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided and results have been developed for systems with outputs in abstract normed linear spaces in order to allow outputs with no delay.

### Partial stochastic asymptotic stability of neutral stochastic functional differential equations with Markovian switching by boundary condition

- Mathematics
- 2012

The partial stochastic asymptotic stability of neutral stochastic functional differential equations with Markovian switching (NSFDEwMSs) has been investigated, the sufficient conditions for partial…

### Stability in part of the variables of “partial” equilibria of systems with aftereffect

- Mathematics
- 2014

The problem of stability in part of the variables of a “partial” equilibrium (this means that a given part of the phase vector coordinates is zero) is considered for nonlinear nonstationary systems…

## References

SHOWING 1-10 OF 25 REFERENCES

### On the asymptotic stability in functional differential equations

- Mathematics
- 1999

Consider a system of functional differential equations dx/dt = f(t, xt) where f is the vector-valued functional. The classical asymptotic stability result for such a system calls for a positive…

### Uniform asymptotic stability in functional differential equations

- Mathematics
- 1978

The classical uniform asymptotic stability result for a system of functional differential equations (l) X' = F(t, xt) calls for a Liapunov functional VQ, 0) satisfying W(14,(0)1) < V(t, 0) <…

### Partial stability and control

- Mathematics
- 1998

From the Publisher:
Partial Stability and Control develops a new, efficient method of analysis and of control synthesis for problems on partial stability and control in dynamic systems described by…

### Theory of Functional Differential Equations

- Mathematics
- 1977

1 Linear differential difference equations.- 1.1 Differential and difference equations.- 1.2 Retarded differential difference equations.- 1.3 Exponential estimates of x(?, f).- 1.4 The characteristic…

### Stability Theory by Liapunov's Direct Method

- Mathematics
- 1977

I. Elements of Stability Theory.- 1. A First Glance at Stability Concepts.- 2. Various Definitions of Stability and Attractivity.- 3. Auxiliary Functions.- 4. Stability and Partial Stability.- 5.…

### Stability theory and the existence of periodic solutions and almost periodic solutions

- Mathematics
- 1975

I. Preliminaries.- 1. Liapunov Functions.- 2. Almost Periodic Functions.- 3. Asymptotically Almost Periodic Functions.- 4. Quasi-Periodic Functions.- 5. Boundary Value Problem.- II. Stability and…

### Principles of mathematical analysis

- Mathematics
- 1964

Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic…