Asymptotic stability of nonautonomous systems by Liapunov's direct method

1995 ◽  
Vol 25 (4) ◽  
pp. 273-280 ◽  
Author(s):  
Dirk Aeyels
Keyword(s):  
Asymptotic Stability ◽  
Direct Method ◽  
Nonautonomous Systems ◽  
Liapunov's Direct Method

Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

1989 ◽  
Vol 56 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Stability ◽  
Material Properties ◽  
Stability Problem ◽  
Large Deflection ◽  
Direct Method ◽  
Rectangular Plates ◽  
Stability Criteria ◽  
The Stability ◽  
Liapunov's Direct Method

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.

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.

Asymptotic stability criteria for delay-differential equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 31-44
Author(s):  
L.C. Becker ◽  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
State Variables ◽  
Stability Criteria ◽  
Bounded State ◽  
Functional Differential ◽  
Delay Differential ◽  
Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

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