Master-Slave Synchronization Using Dynamic Output Feedback

IEEE Trans. Circuits Syst. I

Curran

Chua

1999

171

132

Abstract-In this paper a method for robust synthesis of full static-state error feedback and dynamic-output error feedback for master-slave synchronization of Lur'e systems is presented. Parameter mismatch between the systems is considered in the synchronization schemes. Sufficient conditions for uniform synchronization with a bound on the synchronization error are derived, based on a quadratic Lyapunov function. The matrix inequalities from the case without parameter mismatch between the Lur'e systems remain preserved, but an additional robustness criterion must be taken into account. The robustness criterion is based on an uncertainty relation between the synchronization error bound and the parameter mismatch. The robust synthesis method is illustrated on Chua's circuit with the double scroll. One observes that it is possible to synchronize the master-slave systems up to a relatively small error bound, even in the case of different qualitative behavior between the master and the uncontrolled slave system, such as limit cycles and stable equilibria.

Section: B Dynamic-output Error Feedbackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust synthesis for master-slave synchronization of Lur'e systems

IEEE Trans. Circuits Syst. I

Curran

Chua

1999

171

132

“…The control is based upon the full state vectors x, z. In case there is a lack of full state information dynamic output feedback could be applied to the scheme [Suykens et al, 1997a]. Also observer-based synchronization design is relevant in this context [Morgül & Solak, 1997].…”

Section: Synchronization Schemesmentioning

confidence: 99%

“…Schemes with mutual coupling and master-slave synchronization have been analyzed especially for ad hoc examples of general interest such as Chua's circuit and Lorenz attractor or for classes of nonlinear systems, e.g. Lur'e systems [Chen & Dong, 1998;Wu & Chua, 1994;Kocarev et al, 1993;Suykens et al, 1997aSuykens et al, , 1999. Synchronization schemes have been investigated for identical and nonidentical chaotic systems, including aspects as local and global synchronization, robust synchronization, partial synchronization and generalized synchronization.…”

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization: A Lagrange Programming Network Approach

Int. J. Bifurcation Chaos

Vandewalle

2000

Self Cite

In this paper we interpret chaos synchronization schemes within the framework of Lagrange programming networks, which form a class of continuous-time optimization methods for solving constrained nonlinear optimization problems. From this study it follows that standard synchronization schemes can be regarded as a Lagrange programming network with soft constraining, where synchronization between state vectors is defined as a constraint to the dynamical systems. New schemes are proposed then which implement synchronization by hard and soft constraints within Lagrange programming networks. A version is derived which takes into account synchronization errors within the problem formulation. Furthermore Lagrange programming networks for achieving partial and generalized synchronization are given. The methods assume the existence of potential functions for the given systems. The proposed Lagrange programming networks with hard and soft constraining show improved performance on many simulation examples for identical and nonidentical chaotic systems. The schemes are illustrated on Chua's circuit, Lorenz attractor and n-scroll circuits.

“…This impulsive control law includes static output feedback and linear dynamic output feedback as special cases. The latter method has been discussed in [Suykens et al, 1997a] for a continuous control law. The conditions for synchronization have been expressed as a matrix inequalities [Boyd et al, 1994], which also occur in the context of nonlinear H ∞ synchronization methods for secure communications applications [Suykens et al, 1997c].…”

Section: Introductionmentioning

confidence: 99%

Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback

Int. J. Bifurcation Chaos

Yang

Chua

1998

Self Cite

In this paper we consider impulsive control of master-slave synchronization schemes that consist of identical Lur'e systems. Impulsive control laws are investigated which make use of linear or nonlinear dynamic measurement feedback. A sufficient condition for global asymptotic stability is presented which is characterized by a set of matrix inequalities. Synchronization is proven for the error between the output signals. The method is illustrated on Chua's circuit and a hyperchaotic system with coupled Chua's circuits.