Approximate Values of Time Delay for Quadratic Partial Eigenvalue Assignment Problem

2016 ◽  
Vol 13 (7) ◽  
pp. 4533-4538
Author(s):  
Ehab A El-Sayed ◽  
Mahdy S El-Paoumy
Keyword(s):  
Time Delay ◽  
Assignment Problem ◽  
Eigenvalue Assignment

scholarly journals Partial Eigenvalue Assignment for Gyroscopic Second-Order Systems with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1235
Author(s):  
Hao Liu ◽  
Ranran Li ◽  
Yingying Ding
Keyword(s):  
Time Delay ◽  
Lower Order ◽  
Assignment Problem ◽  
Hadamard Product ◽  
Second Order ◽  
Step Method ◽  
Computational Costs ◽  
The Matrix ◽  
Second Order Systems ◽  
Eigenvalue Assignment

In this paper, the partial eigenvalue assignment problem of gyroscopic second-order systems with time delay is considered. We propose a multi-step method for solving this problem in which the undesired eigenvalues are moved to desired values and the remaining eigenvalues are required to remain unchanged. Using the matrix vectorization and Hadamard product, we transform this problem into a linear systems of lower order, and analysis the computational costs of our method. Numerical results exhibit the efficiency of our method.

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).

scholarly journals On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
El-Sayed M. E. Mostafa ◽  
Abdallah W. Aboutahoun ◽  
Fatma F. S. Omar
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Minimization Problem ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Assignment Problem ◽  
Local Solution ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Eigenvalue Assignment

The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples.

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