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.

Discrete-Delay-Independent and Discrete-Delay-Dependent Criteria for a Class of Neutral Systems

2003 ◽  
Vol 125 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Chang-Hua Lien ◽  
Jenq-Der Chen
Keyword(s):  
Time Delays ◽  
Linear Matrix ◽  
Multiple Time ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Discrete Delay ◽  
Neutral Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
Delay Dependent

In this paper, the asymptotic stability for a class of neutral systems with discrete and distributed multiple time delays is considered. Discrete-delay-independent and discrete-delay-dependent criteria are proposed to guarantee stability for such systems. The resulting stability criteria are written in the form of spectral radius and linear matrix inequality (LMI). Some numerical examples are given to illustrate that our obtained results are less conservative.

scholarly journals The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2120
Author(s):  
Jinxiu Pi ◽  
Hui Yang ◽  
Yadong Shu ◽  
Chongyi Zhong ◽  
Guanghui Yang
Keyword(s):  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stable Strategy ◽  
Two Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Evolutionarily Stable

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

Delay-Dependent Robust Passive Control for Uncertain Discrete Singular Systems with Multiple Time-Delays

2012 ◽  
Vol 433-440 ◽  
pp. 4284-4290
Author(s):  
Shu Hong Tang ◽  
Bo Meng ◽  
Cun Chen Gao
Keyword(s):  
Time Delays ◽  
Passive Control ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Multiple Time ◽  
Weighting Matrix ◽  
Multiple Time Delays ◽  
Discrete Singular Systems ◽  
Delay Dependent

This paper investigates delay-dependent robust passive analysis and control for uncertain discrete singular system with multiple time-delays. Delay-dependent robust passive sufficient condition in terms of linear matrix inequalities (LMI) for the discrete singular systems is obtained by employing Lyapunov-Krasovskii approach and free weighting matrix technique. Based on this condition, a delay-dependent robust passive controller is presented which guarantees the resultant closed-loop system to be regular, casual, stable and robust passive. A numerical example is provided to demonstrate the effectiveness of the method.

Delay-Dependent Absolute Stability Analysis of Lurie Control System with Multiple Delays

2013 ◽  
Vol 631-632 ◽  
pp. 1195-1200
Author(s):  
Yu Bai ◽  
Zhao Di Xu ◽  
Chao Deng ◽  
Chang Liu
Keyword(s):  
Control System ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Stability Criteria ◽  
Multiple Time Delays ◽  
Integral Equality ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper investigates the stability problem for Lurie control system with multiple delays. The system with multiple time-delays is transformed, then the delay divided into several segments, a novel Lyapunov functional is introduced and some new delay-dependent stability criteria are derived by employed integral-equality technique. It is theoretically proved that the obtained criteria are less conservative than some existing ones. An example is given to illustrate the effectiveness of the proposed results.

scholarly journals Fault Detection for Wireless Networked Control Systems with Stochastic Uncertainties and Multiple Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lina Rong ◽  
Chengda Yu ◽  
Pengfei Guo ◽  
Hui Gao
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Time Delays ◽  
Networked Control Systems ◽  
Networked Control ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
System States ◽  
Stochastic Uncertainties

The fault detection problem for a class of wireless networked control systems is investigated. A Bernoulli distributed parameter is introduced in modeling the system dynamics; moreover, multiple time delays arising in the communication are taken into account. The detection observer for tracking the system states is designed, which generates both the state errors and the output errors. By adopting the linear matrix inequality method, a sufficient condition for the stability of wireless networked control systems with stochastic uncertainties and multiple time delays is proposed, and the gain of the fault detection observer is obtained. Finally, an illustrated example is provided to show that the observer designed in this paper tracks the system states well when there is no fault in the systems; however, when fault happens, the observer residual signal rises rapidly and the fault can be quickly detected, which demonstrate the effectiveness of the theoretical results.

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

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

scholarly journals LMI Stability Criterion for Uncertain Systems with Multiple Time Delays

2003 ◽  
Vol 46 (3) ◽  
pp. 1108-1111
Author(s):  
Chang-Hua LIEN ◽  
Jenq Der CHEN ◽  
Ker-Wei YU
Keyword(s):  
Stability Criterion ◽  
Time Delays ◽  
Uncertain Systems ◽  
Multiple Time ◽  
Multiple Time Delays

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

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