scholarly journals Nonlinear Observer Design of the Generalized Rössler Hyperchaotic Systems via DIL Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Exponential Stability ◽  
Decay Rate ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Observer Design ◽  
Nonlinear Observer ◽  
State Observation ◽  
Exponential Decay Rate ◽  
Error System ◽  
Hyperchaotic Systems

The generalized Rössler hyperchaotic systems are presented, and the state observation problem of such systems is investigated. Based on the differential inequality with Lyapunov methodology (DIL methodology), a nonlinear observer design for the generalized Rössler hyperchaotic systems is developed to guarantee the global exponential stability of the resulting error system. Meanwhile, the guaranteed exponential decay rate can be accurately estimated. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of proposed approach.

A SIMPLE OBSERVER OF THE HYPERCHAOTIC RÖSSLER SYSTEM

2010 ◽  
Vol 24 (22) ◽  
pp. 4325-4331
Author(s):  
XING-YUAN WANG ◽  
JUN-MEI SONG
Keyword(s):  
Dynamical System ◽  
Time Domain ◽  
Global Exponential Stability ◽  
Observer Design ◽  
The Other ◽  
State Observation ◽  
Rossler System ◽  
Error System ◽  
Rössler System ◽  
The Time Domain

This paper studies the hyperchaotic Rössler system and the state observation problem of such a system being investigated. Based on the time-domain approach, a simple observer for the hyperchaotic Rössler system is proposed to guarantee the global exponential stability of the resulting error system. The scheme is easy to implement and different from the other observer design that it does not need to transmit all signals of the dynamical system. It is proved theoretically, and numerical simulations show the effectiveness of the scheme finally.

scholarly journals Existence and Global Exponential Stability of Almost Periodic Solutions for SICNNs with Nonlinear Behaved Functions and Mixed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao ◽  
Chuangxia Huang ◽  
Yao Long
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Techniques

By using the Leray-Schauder fixed point theorem and differential inequality techniques, several new sufficient conditions are obtained for the existence and global exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with discrete and distributed delays. The model in this paper possesses two characters: nonlinear behaved functions and all coefficients are time varying. Hence, our model is general and applicable to many known models. Moreover, our main results are also general and can be easily deduced to many simple cases, including some existing results. An example and its simulation are employed to illustrate our feasible results.

HYPERCHAOS GENERATED FROM QI SYSTEM AND ITS OBSERVER

2009 ◽  
Vol 23 (07) ◽  
pp. 963-974 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAOXIAN ZHANG ◽  
YONGFENG GAO
Keyword(s):  
Dynamical System ◽  
Time Domain ◽  
Global Exponential Stability ◽  
Observer Design ◽  
The Other ◽  
The Novel ◽  
Nonlinear Controller ◽  
Error System ◽  
The Time Domain ◽  
Lyapunov Exponent Spectrum

This paper reports a novel four-dimensional hyperchaos generated from Qi system, obtained by adding nonlinear controller to Qi chaos system. The novel hyperchaos is studied by bifurcation diagram, Lyapunov exponent spectrum and phase diagram. Numerical simulations show that the new system's behavior can be periodic, chaotic and hyperchaotic as the parameter varies. Based on the time-domain approach, a simple observer for the hyperchaotic is proposed to guarantee the global exponential stability of the resulting error system. The scheme is easy to implement and different from the other observer design since it does not need to transmit all signals of the dynamical system.

scholarly journals Dynamic Analysis of Nonlinear Impulsive Neutral Nonautonomous Differential Equations with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jinxian Li
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Exponential Stability ◽  
Dynamic Analysis ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Lyapunov Functionals ◽  
Nonautonomous Differential Equations ◽  
Inequality Technique

A class of neural networks described by nonlinear impulsive neutral nonautonomous differential equations with delays is considered. By means of Lyapunov functionals and differential inequality technique, criteria on global exponential stability of this model are derived. Many adjustable parameters are introduced in criteria to provide flexibility for the design and analysis of the system. The results of this paper are new and they supplement previously known results. An example is given to illustrate the results.

scholarly journals Anticollocated Backstepping Observer Design for a Class of Coupled Reaction-Diffusion PDEs

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Antonello Baccoli ◽  
Alessandro Pisano
Keyword(s):  
Explicit Form ◽  
Reaction Diffusion ◽  
Observer Design ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
State Observation ◽  
Fast Convergence Rate ◽  
Error System ◽  
Coupled Reaction ◽  
Diffusivity Parameter

The state observation problem is tackled for a system ofncoupled reaction-diffusion PDEs, possessing the same diffusivity parameter and equipped with boundary sensing devices. Particularly, a backstepping-based observer is designed and the exponential stability of the error system is proven with an arbitrarily fast convergence rate. The transformation kernel matrix is derived in the explicit form by using the method of successive approximations, thereby yielding the observer gains in the explicit form, too. Simulation results support the effectiveness of the suggested design.

scholarly journals Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

2013 ◽  
Vol 23 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Yang Liu ◽  
Rongjiang Yang ◽  
Jianquan Lu ◽  
Bo Wu ◽  
Xiushan Cai
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
High Order ◽  
Impulsive Effect ◽  
Time Varying ◽  
Stability Criteria ◽  
Globally Exponential Stability ◽  
Impulsive Differential Inequality

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

scholarly journals Existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Jing Liu
Keyword(s):  
Neural Network ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
High Order ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem

AbstractSufficient conditions are obtained for the existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses by using Mawhin’s continuation theorem of coincidence degree and by means of a method based differential inequality.

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