Lyapunov Matrices for the Stability Analysis of a Multiple Distributed Time-Delay System with Piecewise-Function Kernel

2018 ◽  
Author(s):  
Luis Juarez ◽  
Sabine Mondie
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
Piecewise Function ◽  
Distributed Time Delay ◽  
The Stability

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty

2015 ◽  
Vol 58 ◽  
pp. 50-57 ◽  
Author(s):  
Rajeeb Dey ◽  
Sandip Ghosh ◽  
Goshaidas Ray ◽  
Anjan Rakshit ◽  
Valentina Emilia Balas
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
Bounded Uncertainty

On the stability bifurcation of a nonlinear time delay system

Automatica ◽  
1998 ◽  
Vol 34 (3) ◽  
pp. 375-378 ◽  
Author(s):  
Mustapha S. Fofana ◽  
David J. Lamb
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
The Stability

scholarly journals Synchronization approach for chaotic time-varying delay system based on Wirtinger inequality

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668902
Author(s):  
Zhanshan Zhao ◽  
Meili He ◽  
Jing Zhang ◽  
Guowei Xu
Keyword(s):  
Time Delay ◽  
Stability Criterion ◽  
Delay System ◽  
Jensen Inequality ◽  
Time Delay System ◽  
Control Approach ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Varying Delay

A novel control approach based on Wirtinger inequality is designed for nonlinear chaos synchronization time delay system. In order to reduce the conservatism for the stability criterion, a Lyapunov–Krasovskii functional with triple-integral term is constructed. The improved Wirtinger inequality is used to reduce the conservative which is caused by Jensen inequality, and a stability criterion is proposed by reciprocally convex method. Furthermore, a state feedback controller is designed to synchronize the master-slave systems based on the proposed criteria through cone complementary linearization approach. Finally, a simulation for Lorenz chaos time delay system is given to prove the validity based on the proposed synchronization control approach.

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