On the Lyapunov stability theory for impulsive dynamical systems

2019 ◽  
pp. 1
Author(s):  
Everaldo Mello Bonotto ◽  
Ginnara M. Souto
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory

On One Approach to the Control of Uncertain Systems

1993 ◽  
Vol 115 (2B) ◽  
pp. 373-380 ◽  
Author(s):  
G. Leitmann
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Uncertain Systems ◽  
Lyapunov Stability Theory ◽  
Personal History ◽  
The Past ◽  
History Of ◽  
Control Of Uncertain Systems

This paper is a personal history of one area of research with which I have been concerned over the past twenty years and which continues to attract my albeit waning attention, the control of dynamical systems based on uncertain models. Thus, it is a subjective account of various factors which I believe to have steered me to approach the problem via a constructive use of Lyapunov stability theory.

scholarly journals Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches

2017 ◽  
Vol 7 (3) ◽  
pp. 248-254
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

The main objective of this work is to discuss a generalized synchronization of a coupled chaotic identicaland nonidentical dynamical systems. We propose a method used to study generalized synchronization in masterslavesystems. This method, is based on the classical Lyapunov stability theory, utilizes the master continuous timechaotic system to monitor the synchronized motions. Various numerical simulations are performed to verify theeffectiveness of the proposed approach.

On the Dynamics of the Chaotic General Lorenz System

2017 ◽  
Vol 27 (05) ◽  
pp. 1750075 ◽  
Author(s):  
Fuchen Zhang ◽  
Xiaofeng Liao ◽  
Yi-An Chen ◽  
Chunlai Mu ◽  
Guangyun Zhang
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Stability ◽  
Current Literature ◽  
Stability Theory ◽  
Lyapunov Functions ◽  
Lorenz System ◽  
Optimization Theory ◽  
Lyapunov Stability Theory ◽  
Attractive Sets

In this paper, the global attractive sets of the general Lorenz system are studied based on the Lyapunov stability theory and optimization theory. The innovation of this paper lies in that the method of constructing Lyapunov functions applied to many other dynamical systems is not applicable to this general Lorenz system. Comparing with the best results in the current literature, our new results fill the gap of the estimate for the case of [Formula: see text], [Formula: see text], [Formula: see text]

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

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