scholarly journals A NONLINEAR STATE FEEDBACK APPROACH TO THE CONTROL AND SYNCHRONIZATION OF CONTINUOUS-TIME CHAOTIC SYSTEMS

1999 ◽  
Vol 48 (9) ◽  
pp. 1618
Author(s):  
GAO JIN-FENG ◽  
LUO XIAN-JUE ◽  
MA XI-KUI ◽  
PAN XIU-QIN ◽  
WANG JUN-KUN
Keyword(s):  
Continuous Time ◽  
State Feedback ◽  
Chaotic Systems ◽  
Control And Synchronization ◽  
Nonlinear State

Disturbed Chaotic Systems Synchronization via Robust Mixed Functional Projective Method

2014 ◽  
Vol 496-500 ◽  
pp. 1293-1297
Author(s):  
Tao Fan ◽  
Ning Fang ◽  
Fei Tan
Keyword(s):  
State Feedback ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Generalized Synchronization ◽  
Linear State ◽  
Control And Synchronization

Robust mixed functional projective synchronization (RMFPS), which is the generalized synchronization idea developed very recently, is investigated in this paper. Based on Lyapunov stability theory and linear matrix inequality (LMI), some novel stability criterions for the synchronization between drive and response chaotic systems with disturbances are derived, and then a simple linear state feedback synchronization controller is designed. In order to test the proposed method, numerical simulations of hyper-chaotic unified systems with disturbances are then provided to show the effectiveness and feasibility of this chaos control and synchronization schemes.

scholarly journals Positivity and Linearization of a Class of Nonlinear Continuous–Time Systems by State Feedbacks

2015 ◽  
Vol 25 (4) ◽  
pp. 827-831 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Nonlinear State ◽  
Continuous Time System

Abstract The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.

SYNCHRONIZING CONTINUOUS TIME CHAOTIC SYSTEMS OVER NONDETERMINISTIC NETWORKS WITH PACKET DROPOUTS

2012 ◽  
Vol 22 (12) ◽  
pp. 1250300 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TORRES
Keyword(s):  
Continuous Time ◽  
Chaotic Systems ◽  
Random Fluctuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Packet Dropouts ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Varying Delay

The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

Controlling Actively Q-Switched Laser Output by Nonlinear State Feedback

2013 ◽  
Vol 53 (4) ◽  
pp. 151-160 ◽  
Author(s):  
M. Thitsa ◽  
W. S. Gray
Keyword(s):  
State Feedback ◽  
Laser Output ◽  
Nonlinear State
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