Methods for Studying the Stability of Linear Periodic Systems Depending on a Small Parameter

2021 ◽  
Author(s):  
M. G. Yumagulov ◽  
L. S. Ibragimova ◽  
A. S. Belova
Keyword(s):  
Small Parameter ◽  
Periodic Systems ◽  
The Stability ◽  
Linear Periodic Systems

A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling

1993 ◽  
Vol 115 (1) ◽  
pp. 1-8 ◽  
Author(s):  
I. Minis ◽  
R. Yanushevsky
Keyword(s):  
Infinite Order ◽  
Transfer Functions ◽  
Milling Process ◽  
Periodic Systems ◽  
Time Varying ◽  
Machine Tool Chatter ◽  
Constant Coefficients ◽  
The Stability ◽  
Linear Periodic Systems ◽  
Standard Techniques

A new method for the prediction of chatter in milling is presented. The dynamics of the milling process are described by a set of differential-difference equations with time varying periodic coefficients. The stability of this system is examined using Fourier analysis and basic properties of the parametric transfer functions of linear periodic systems. The resulting characteristic equation is of infinite order and has constant coefficients. Its truncated version is used to determine the limit of stability employing standard techniques of control theory. The proposed method is applied to a theoretical example and a practical milling system.

Parametric Frequency Response of Linear Periodic Systems - Theory and Experiment

2001 ◽  
Vol 34 (12) ◽  
pp. 13-18
Author(s):  
B.P. Lampe ◽  
S.K. Volovodov ◽  
E.N. Rosenwasser ◽  
A.V. Smolnikov
Keyword(s):  
Frequency Response ◽  
Systems Theory ◽  
Periodic Systems ◽  
Linear Periodic Systems ◽  
Theory And Experiment ◽  
Parametric Frequency

H-Controllability and Observability of Linear Periodic Systems

1984 ◽  
Vol 22 (6) ◽  
pp. 889-893 ◽  
Author(s):  
Sergio Bittanti ◽  
Patrizio Colaneri ◽  
Guido Guardabassi
Keyword(s):  
Periodic Systems ◽  
Linear Periodic Systems ◽  
Controllability And Observability

Generalized Bezoutian for Discrete-Time Linear Periodic Systems

1992 ◽  
Vol 25 (21) ◽  
pp. 36-39
Author(s):  
Carmen Coll ◽  
Rafael Bru ◽  
Vicente Heranández
Keyword(s):  
Discrete Time ◽  
Periodic Systems ◽  
Linear Periodic Systems ◽  
Time Linear

Zeros of a Class of Transcendental Equation with Application to Bifurcation of DDE

2016 ◽  
Vol 26 (04) ◽  
pp. 1650062 ◽  
Author(s):  
Kit Ian Kou ◽  
Yijun Lou ◽  
Yong-Hui Xia
Keyword(s):  
Small Parameter ◽  
Climate Changes ◽  
Transcendental Equation ◽  
Bifurcation Parameter ◽  
Parameter Perturbation ◽  
Distribution Of Zeros ◽  
World Model ◽  
The Real ◽  
Stability And Bifurcations ◽  
The Stability

Zeros of a class of transcendental equation with small parameter [Formula: see text] are considered in this paper. There have been many works in the literature considering the distribution of zeros of the transcendental equation by choosing the delay [Formula: see text] as bifurcation parameter. Different from standard consideration, we choose [Formula: see text] as bifurcation parameter (not the delay [Formula: see text]) to discuss the distribution of zeros of such transcendental equation. After mathematical analysis, the obtained results are successfully applied to the bifurcation analysis in a biological model in the real word phenomenon. In the real world model, the effect of climate changes can be seen as the small parameter perturbation, which can induce bifurcations and instability. We present two methods to analyze the stability and bifurcations.

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