Sufficient conditions for inverse anticipating synchronization of unidirectional coupled chaotic systems with multiple time delays

2010 ◽  
Author(s):  
Jie Li ◽  
Pengzhen Dong ◽  
Gang Shang
Keyword(s):  
Time Delays ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Multiple Time ◽  
Multiple Time Delays

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

Robust stability of uncertain linear systems with multiple time delays

1997 ◽  
Vol 211 (3) ◽  
pp. 195-202
Author(s):  
Y Fang
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Time Delays ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Multiple Time Delays ◽  
Uncertain Linear Systems

In this paper, the robust stability of uncertain linear systems with multiple time delays is studied. Sufficient conditions for robust stability of linear time delay systems with convex perturbations are obtained. From these sufficient conditions, a few results on robust stability of systems with other perturbations are derived. Some previously known sufficient conditions are generalized.

Zero-lag synchronization and multiple time delays in two coupled chaotic systems

2010 ◽  
Vol 81 (3) ◽  
Author(s):  
Meital Zigzag ◽  
Maria Butkovski ◽  
Anja Englert ◽  
Wolfgang Kinzel ◽  
Ido Kanter
Keyword(s):  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Lag Synchronization ◽  
Multiple Time Delays

scholarly journals Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays

2016 ◽  
Vol 26 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Multiple Time ◽  
Multiple Time Delays

Abstract Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.

Stability analysis of connected vehicles with V2V communication and time delays: CTCR method via Bézout’s resultant

2021 ◽  
pp. 014233122098142
Author(s):  
Sirin Akkaya ◽  
Onur Akbati ◽  
Ali Fuat Ergenc
Keyword(s):  
Characteristic Equation ◽  
Time Delays ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Connected Vehicles ◽  
Multiple Time ◽  
String Stability ◽  
V2v Communication ◽  
Multiple Time Delays ◽  
Input Delays

This paper is focused on the distributed control of connected vehicles via vehicle-to-vehicle (V2V) communication. A mixed predecessor following topology with a virtual leader under constant time headway policy is analysed in case of communication and input delays. The longitudinal dynamics of each vehicle in the platoon is represented by a third-order linear model. Unavoidable communication and input delays are introduced into the platoon structure which converts the characteristic equation of the system into a transcendental type. The stability regions of the system in delay space are obtained by utilizing the cluster treatment of characteristic root (CTCR) method in the case of single and multiple time delays. A new Bézout resultant matrix-based approach is proposed to determine the kernel and offspring hypersurfaces of the CTCR method. The determination of these kernel and offspring hypersurfaces becomes computational costly as the number of vehicles increases in the platoon due to the increasing degree of characteristic equation. However, the proposed method reduces the dimensions of the coefficient matrix which is created by using the characteristic equation. It is concluded that the proposed method confirms the internal stability of the connected vehicles with both generic information flow topologies and formation between vehicles under single and multiple time delays. Thereafter, a local string stability definition is proposed in terms of spacing errors. Sufficient conditions to obtain string stability under mixed predecessor following topology for the existence and nonexistence of time delay are given. Finally, several simulation studies with different scenarios are conducted to display the effectiveness of the proposed model and method for internal and string stabilities.

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

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