Linear Delay Systems with Cone Invariance

2017 ◽  
pp. 95-105
Author(s):  
Jun Shen
Keyword(s):  
Delay Systems ◽  
Linear Delay ◽  
Cone Invariance

Stability analysis of linear delay systems with cone invariance

Automatica ◽  
2015 ◽  
Vol 53 ◽  
pp. 30-36 ◽  
Author(s):  
Jun Shen ◽  
Wei Xing Zheng
Keyword(s):  
Stability Analysis ◽  
Delay Systems ◽  
Linear Delay ◽  
Cone Invariance

Polyhedral approximation method for reachable sets of linear delay systems

2020 ◽  
Vol 14 (12) ◽  
pp. 1548-1556
Author(s):  
Renhong Hu ◽  
Lizhen Shao ◽  
Yuhao Cong
Keyword(s):  
Approximation Method ◽  
Reachable Sets ◽  
Delay Systems ◽  
Polyhedral Approximation ◽  
Linear Delay

scholarly journals On the Notion of Duality for Linear Delay Systems

1998 ◽  
Vol 31 (19) ◽  
pp. 25-30
Author(s):  
H. Mounier ◽  
J. Rudolph
Keyword(s):  
Delay Systems ◽  
Linear Delay

Eigenvalue Assignment for Control of Time-Delay Systems Via the Generalized Runge–Kutta Method

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
JinBo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Time Delay ◽  
Optimization Techniques ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Kutta Method ◽  
Feedback Controllers ◽  
Runge Kutta Method ◽  
Linear Delay ◽  
Runge Kutta ◽  
Eigenvalue Assignment

This paper presents an eigenvalue assignment method for the time-delay systems with feedback controllers. A new form of Runge–Kutta algorithm, generalized from the classical fourth-order Runge–Kutta method, is utilized to stabilize the linear delay differential equation (DDE) with a single delay. Pole placement of the DDEs is achieved by assigning the eigenvalue with maximal modulus of the Floquet transition matrix obtained via the generalized Runge–Kutta method (GRKM). The stabilization of the DDEs with feedback controllers is studied from the viewpoint of optimization, i.e., the DDEs are controlled through optimizing the feedback gain matrices with proper optimization techniques. Several numerical cases are provided to illustrate the feasibility of the proposed method for control of linear time-invariant delayed systems as well as periodic-coefficient ones. The proposed method is verified with high computational accuracy and efficiency through comparing with other methods such as the Lambert W function and the semidiscretization method (SDM).

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