SL(3,R) as the group of symmetry transformations for all one‐dimensional linear systems. III. Equivalent Lagrangian formalisms

1992 ◽  
Vol 33 (5) ◽  
pp. 1571-1578 ◽  
Author(s):  
M. Aguirre ◽  
C. Friedli ◽  
J. Krause
Keyword(s):  
Linear Systems ◽  
One Dimensional ◽  
Symmetry Transformations

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

scholarly journals Revisiting the 1D and 2D Laplace Transforms

2020 ◽  
Author(s):  
Manuel Duarte Ortigueira ◽  
José Tenreiro Machado
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Linear Systems ◽  
Laplace Transforms ◽  
Dimensional Case ◽  
Initial Condition ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

Controller Gain Design of 2-D Linear Systems Based on the Existing 1-D Analytical Solution

2013 ◽  
Vol 681 ◽  
pp. 55-59
Author(s):  
Wen Jeng Liu
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Two Dimensional ◽  
Numerical Examples ◽  
One Dimensional ◽  
Controller Gain ◽  
Necessary And Sufficient

Abstract. A controller gain design problem of two-dimensional (2-D) linear systems is proposed in this paper. For one-dimensional (1-D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the feedback gain is given by [1]. Based on the existing 1-D analytical solution, a 2-D state feedback controller gain can be designed to achieve the desired poles. Finally, two numerical examples are shown to exhibit the validity of the proposed approach.

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