A Theory for Singularity and Stability in Two-dimensional Linear Systems

2022 ◽  
Vol 6 (1) ◽  
pp. 63-105
Author(s):  
Albert C. J. Luo
Keyword(s):  
Linear Systems ◽  
Two Dimensional

On the Bose-Trautman condition for stability of two-dimensional linear systems

1998 ◽  
Vol 46 (7) ◽  
pp. 2069-2070 ◽  
Author(s):  
Yangfeng Su ◽  
A. Bhaya
Keyword(s):  
Linear Systems ◽  
Two Dimensional

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

scholarly journals Features of the construction of information transfer system which using two-dimensional signals

2019 ◽  
Vol 30 ◽  
pp. 04008
Author(s):  
Andrey Degtyaryov ◽  
Vera Miryanova
Keyword(s):  
Linear Systems ◽  
Information Transfer ◽  
Transfer System ◽  
Two Dimensional ◽  
Orthogonal Functions ◽  
Prototype Filter ◽  
Interchannel Interference ◽  
Low Pass ◽  
Impulse Characteristics ◽  
Coordinate Basis

The article deals with analysis of the causes of intersymbol interference and interchannel interference. It is indicated that physically unrealizable orthogonal bases are used to describe systems and signals. The considered interference occurs due to the loss of orthogonality by the coordinate signals of the bases. Known methods for obtaining systems of orthogonal functions do not allow the formation of a coordinate basis corresponding to physically feasible systems and signals. It is proposed to use equidistant biased impulse characteristics of physically realizable linear systems as basic signals. An orthogonalization method based on determining the weight of orthogonality is described. It is shown that the resulting basis is quasi-orthogonal. It is determined that the conversion of the standart low-pass prototype filter into the filters of channel-forming equipment does not change the conditions of orthogonality. Structural schemes of a modulator and a demodulator of two-dimensional signals are proposed, based on the developed method of orthogonalization.

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.

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