On the stability of a class of linear systems with distributed and lumped parameter

2018 ◽  
Vol 82 (6) ◽  
pp. 757-766
Author(s):  
B. Bairamov ◽  
◽  
F. Bairamov ◽  
Keyword(s):  
Linear Systems ◽  
Lumped Parameter ◽  
The Stability

scholarly journals The stability of parametricdifference linear systems

2004 ◽  
Vol 17 (10) ◽  
pp. 1167-1169 ◽  
Author(s):  
M.C. Casabán ◽  
J.L. Morera ◽  
G. Rubio ◽  
G.A. Ossandón
Keyword(s):  
Linear Systems ◽  
The Stability

scholarly journals On the Stability of Switched Positive Linear Systems

2007 ◽  
Vol 52 (6) ◽  
pp. 1099-1103 ◽  
Author(s):  
L. Gurvits ◽  
R. Shorten ◽  
O. Mason
Keyword(s):  
Linear Systems ◽  
The Stability

Application of Center Manifold Theory to Regulation of a Flexible Beam

1997 ◽  
Vol 119 (2) ◽  
pp. 158-165 ◽  
Author(s):  
Amir Khajepour ◽  
M. Farid Golnaraghi ◽  
Kirsten A. Morris
Keyword(s):  
Control Strategy ◽  
Center Manifold ◽  
Flexible Beam ◽  
Trial And Error ◽  
Center Manifold Theory ◽  
Control Techniques ◽  
Lumped Parameter ◽  
The Stability ◽  
Frequency Relationship ◽  
Manifold Theory

In this paper we consider the problem of regulation of a flexible lumped parameter beam. The controller is an active/passive mass-spring-dashpot mechanism which is free to slide along the beam. In this problem the plant/controller equations are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes associated with a pair of pure imaginary eigenvalues. As a result, linear control techniques as well as most conventional nonlinear control techniques can not be applied. In earlier studies Golnaraghi (1991) and Golnaraghi et al. (1994) a control strategy based on Internal resonance was developed to transfer the oscillatory energy from the beam to the slider, where it was dissipated through controller damping. Although these studies provided very good understanding of the control strategy, the analytical method was based on perturbation techniques and had many limitations. Most of the work was based on numerical techniques and trial and error. In this paper we use center manifold theory to address the shortcomings of the previous studies, and extend the work to a more general control law. The technique is based on reducing the dimension of system and simplifying the nonlinearities using center manifold and normal forms techniques, respectively. The simplified equations are used to investigate the stability and to develop a relation for the optimal controller/plant natural frequencies at which the maximum transfer of energy occurs. One of the main contributions of this work is the elimination of the trial and error and inclusion of damping in the optimal frequency relationship.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

On the stability of linear systems with fractional-order elements

2009 ◽  
Vol 40 (5) ◽  
pp. 2317-2328 ◽  
Author(s):  
A.G. Radwan ◽  
A.M. Soliman ◽  
A.S. Elwakil ◽  
A. Sedeek
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
The Stability

scholarly journals An iterative frequency-sweeping approach for stability analysis of linear systems with multiple delays

2017 ◽  
Vol 36 (2) ◽  
pp. 379-398
Author(s):  
Xu-Guang Li ◽  
Silviu-Iulian Niculescu ◽  
Arben Çela
Keyword(s):  
Stability Analysis ◽  
Asymptotic Behaviour ◽  
Linear Systems ◽  
Invariance Property ◽  
Multiple Delays ◽  
Numerical Examples ◽  
The Stability ◽  
Imaginary Roots ◽  
Frequency Sweeping

AbstractIn this article, we study the stability of linear systems with multiple (incommensurate) delays, by extending a recently proposed frequency-sweeping approach. First, we consider the case where only one delay parameter is free while the others are fixed. The complete stability w.r.t. the free delay parameter can be systematically investigated by proving an appropriate invariance property. Next, we propose an iterative frequency-sweeping approach to study the stability under any given multiple delays. Moreover, we may effectively analyse the asymptotic behaviour of the critical imaginary roots (if any) w.r.t. each delay parameter, which provides a possibility for stabilizing the system through adjusting the delay parameters. The approach is simple (graphical test) and can be applied systematically to the stability analysis of linear systems including multiple delays. A deeper discussion on its implementation is also proposed. Finally, various numerical examples complete the presentation.

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