General theorems on the structure and the splitting off of elementary factors of analytic matrix-valued functions

1988 ◽  
pp. 9-14
Author(s):  
V. P. Potapov
Keyword(s):  
Analytic Matrix

scholarly journals Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

2006 ◽  
Vol 418 (1) ◽  
pp. 315-335 ◽  
Author(s):  
Wim Michiels ◽  
Kirk Green ◽  
Thomas Wagenknecht ◽  
Silviu-Iulian Niculescu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Matrix Functions ◽  
Time Delay Systems ◽  
Analytic Matrix ◽  
Stability Radii

scholarly journals Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems I: Small and Medium Amplitude Oscillations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3287
Author(s):  
Elena Hernandez ◽  
Octavio Manero ◽  
Fernando Bautista ◽  
Juan Paulo Garcia-Sandoval
Keyword(s):  
Dynamical Systems ◽  
Frequency Response ◽  
Harmonic Balance ◽  
Matrix Method ◽  
Series Solution ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Analytic Matrix ◽  
Solution Methods ◽  
Traditional Approaches

This is the first on a series of articles that deal with nonlinear dynamical systems under oscillatory input that may exhibit harmonic and non-harmonic frequencies and possibly complex behavior in the form of chaos. Frequency response techniques of nonlinear dynamical systems are usually analyzed with numerical methods because, most of the time, analytical solutions turn out to be difficult, if not impossible, since they are based on infinite series of trigonometric functions. The analytic matrix method reported here is a direct one that speeds up the solution processing compared to traditional series solution methods. In this method, we work with the invariant submanifold of the problem, and we propose a series solution that is equivalent to the harmonic balance series solution. However, the recursive relation obtained for the coefficients in our analytical method simplifies traditional approaches to obtain the solution with the harmonic balance series method. This method can be applied to nonlinear dynamic systems under oscillatory input to find the analog of a usual Bode plot where regions of small and medium amplitude oscillatory input are well described. We found that the identification of such regions requires both the amplitude as well as the frequency to be properly specified. In the second paper of the series, the method to solve problems in the field of large amplitudes will be addressed.

scholarly journals Approximation by Analytic Matrix Functions: The Four Block Problem

1997 ◽  
Vol 148 (1) ◽  
pp. 191-228 ◽  
Author(s):  
V.V. Peller ◽  
S.R. Treil
Keyword(s):  
Matrix Functions ◽  
Analytic Matrix

Null Structure for Analytic Matrix Functions

1990 ◽  
pp. 7-39
Author(s):  
Joseph A. Ball ◽  
Israel Gohberg ◽  
Leiba Rodman
Keyword(s):  
Matrix Functions ◽  
Analytic Matrix
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