scholarly journals On the Asymptotic Stability of Stochastic Nonlinear Dynamical Systems with Random Parameters

1978 ◽  
Vol 44 (380) ◽  
pp. 1234-1241
Author(s):  
Yoshifumi SUNAHARA ◽  
Toshiyuki ASAKURA ◽  
Yohji MORITA
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Random Parameters ◽  
Nonlinear Dynamical

scholarly journals State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1424 ◽  
Author(s):  
Angelo Alessandri ◽  
Patrizia Bagnerini ◽  
Roberto Cianci
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Estimation Error ◽  
Stability Conditions ◽  
Nonlinear Dynamical ◽  
State Observation ◽  
State Observers ◽  
The Stability

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

scholarly journals STABILITY AND STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS

2017 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
P. Sattayatham ◽  
R. Saelim ◽  
S. Sujitjorn
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Feedback Controllers ◽  
Nonlinear Dynamical ◽  
System A ◽  
Continuous Feedback ◽  
Stability And Stabilization ◽  
The Stability

Exponential and asymptotic stability for a class of nonlinear dynamical systems with uncertainties is investigated.  Based on the stability of the nominal system, a class of bounded continuous feedback controllers is constructed.  By such a class of controllers, the results guarantee exponential and asymptotic stability of uncertain nonlinear dynamical system.  A numerical example is also given to demonstrate the use of the main result.

scholarly journals Chaos and Complexity Dynamics of Evolutionary Systems

2020 ◽  
Author(s):  
Lal Mohan Saha
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Chaotic Motion ◽  
Correlation Dimension ◽  
Nonlinear Dynamical Systems ◽  
Chaotic Attractors ◽  
Tabular Form ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical

Chaotic phenomena and presence of complexity in various nonlinear dynamical systems extensively discussed in the context of recent researches. Discrete as well as continuous dynamical systems both considered here. Visualization of regularity and chaotic motion presented through bifurcation diagrams by varying a parameter of the system while keeping other parameters constant. In the processes, some perfect indicator of regularity and chaos discussed with appropriate examples. Measure of chaos in terms of Lyapunov exponents and that of complexity as increase in topological entropies discussed. The methodology to calculate these explained in details with exciting examples. Regular and chaotic attractors emerging during the study are drawn and analyzed. Correlation dimension, which provides the dimensionality of a chaotic attractor discussed in detail and calculated for different systems. Results obtained presented through graphics and in tabular form. Two techniques of chaos control, pulsive feedback control and asymptotic stability analysis, discussed and applied to control chaotic motion for certain cases. Finally, a brief discussion held for the concluded investigation.

Asymptotic stability of distributed order nonlinear dynamical systems

2017 ◽  
Vol 48 ◽  
pp. 541-549 ◽  
Author(s):  
G. Fernández-Anaya ◽  
G. Nava-Antonio ◽  
J. Jamous-Galante ◽  
R. Muñoz-Vega ◽  
E.G. Hernández-Martínez
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
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