Detecting coexisting oscillatory patterns in delay coupled Lur’e systems

This Letter proposes a new synchronization theorem for a subclass of chaotic Lur'e systems. We take a specific state variable of the drive system as the driving signal. We prove that globally synchronization can be attained via the simple linear error feedback. The approach is illustrated using Chua's chaotic oscillator and a hyperchaotic oscillator.

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Improved stability criteria for neutral type Lur’e systems with time-varying delays

Applied Mathematics Letters ◽

10.1016/j.aml.2014.07.024 ◽

2014 ◽

Vol 38 ◽

pp. 168-173 ◽

Cited By ~ 10

Author(s):

R. Sivasamy ◽

R. Rakkiyappan

Keyword(s):

Neutral Type ◽

Time Varying ◽

Stability Criteria ◽

Lur’E Systems ◽

Improved Stability

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Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

Abstract and Applied Analysis ◽

10.1155/2012/961382 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18

Author(s):

W. Weera ◽

P. Niamsup

Keyword(s):

Neutral Type ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Lur’E Systems ◽

Interval Time ◽

Delay Function ◽

Time Varying Delay ◽

Bounded Nonlinearity ◽

Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

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DELAY-DEPENDENT SYNCHRONIZATION CRITERION FOR LUR'E SYSTEMS WITH DELAY FEEDBACK CONTROL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016677 ◽

2006 ◽

Vol 16 (10) ◽

pp. 3087-3091 ◽

Cited By ~ 40

Author(s):

YONG HE ◽

GUILIN WEN ◽

QING-GUO WANG

Keyword(s):

Time Delay ◽

Delay Systems ◽

Matrix Approach ◽

Time Delay Systems ◽

Stability Studies ◽

Lur’E Systems ◽

Weighting Matrix ◽

Delay Feedback Control ◽

Delay Dependent ◽

Synchronization Scheme

A master-slave synchronization scheme for Lur'e systems is studied for a known delay existing between master and slave systems. Based on the latest development of stability studies for time-delay systems, a new delay-dependent synchronization criterion is derived by the free-weighting matrix approach. The criterion shown by example is less conservative than the existing synchronization criteria.

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