Control of the Hopf Bifurcation by a Linear Feedback Control

2015 ◽  
Vol 25 (01) ◽  
pp. 1550006 ◽  
Author(s):  
J. A. López-Renteria ◽  
F. Verduzco ◽  
B. Aguirre-Hernández
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Linear State

In this work, we design a kind of linear state feedback control, via the roots connecting-curve, for a class of nonlinear systems which permits to control the Hopf bifurcation. An illustrative example is given.

scholarly journals State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Control Method ◽  
Input Saturation ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Feedback Control Method ◽  
Linear State

We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

fuzzy state-feedback control design for nonlinear systems with -stability constraints: An LMI approach

2008 ◽  
Vol 78 (4) ◽  
pp. 514-531 ◽  
Author(s):  
Wudhichai Assawinchaichote ◽  
Sing Kiong Nguang ◽  
Peng Shi ◽  
El-Kébir Boukas
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Control Design ◽  
State Feedback Control ◽  
Lmi Approach ◽  
Fuzzy State

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

2013 ◽  
Vol 275-277 ◽  
pp. 2565-2569
Author(s):  
Lin Xu ◽  
Zhong Liu ◽  
Yun Chen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Numerical Example ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

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