New Theorem for Asymptotically Stability for Time-Delayed Systems Based on LMI

2013 ◽  
Vol 433-435 ◽  
pp. 1086-1090
Author(s):  
Chang Hui Song
Keyword(s):  
Time Delays ◽  
Asymptotical Stability ◽  
Multiple Time ◽  
Sufficient Condition ◽  
Delayed Systems ◽  
New Approach ◽  
Multiple Time Delays ◽  
Asymptotical Stable ◽  
Delay Dependent

This paper stadies the problem of the asymptotical stability for a time-delayed systems. By using LMI method, a new approach is used to derive a delay-dependent sufficient condition, which can guarantee that the time-delayed systems with multiple time delays is asymptotical stable. At last, a numberical example is given to show that the new theorem is more effective than the present methods.

Delay-Dependent Stability Control for Power System With Multiple Time-Delays

2016 ◽  
Vol 31 (3) ◽  
pp. 2316-2326 ◽  
Author(s):  
Jian Li ◽  
Zhaohui Chen ◽  
Dongsheng Cai ◽  
Wei Zhen ◽  
Qi Huang
Keyword(s):  
Power System ◽  
Time Delays ◽  
Stability Control ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability

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.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

Bifurcation, Synchronization, and Multistability of Two Interacting Networks with Multiple Time Delays

2016 ◽  
Vol 26 (09) ◽  
pp. 1650156 ◽  
Author(s):  
Xiaochen Mao
Keyword(s):  
Time Delays ◽  
Nearest Neighbor ◽  
Pitchfork Bifurcation ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Trivial Equilibrium ◽  
Dynamical Properties ◽  
Interacting Networks ◽  
Delay Dependent ◽  
Theoretical Results

This paper reveals the dynamical properties of two interacting neural networks with multiple couplings. Different time delays are introduced into the nearest-neighbor links and long-range connections in each layer and the couplings between different substructures. The delay-dependent and delay-independent stability and the oscillations bifurcated from the trivial equilibrium of the network are analyzed. The conditions of the existence of nontrivial equilibria and pitchfork bifurcation are discussed. Numerical simulations are performed to validate the theoretical results and interesting neuronal activities are observed, such as completely synchronous oscillations, three types of asynchronous oscillations, multiple switches between the rest states and different oscillations, coexistence of different oscillations, and coexistence of nontrivial equilibria and oscillations.

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