scholarly journals Considerations regarding input and output spaces for time-varying dynamical systems

1977 ◽  
Vol 4 (1) ◽  
pp. 365-384 ◽  
Author(s):  
William L. Root
Keyword(s):  
Dynamical Systems ◽  
Time Varying ◽  
Input And Output

Reduction of Arbitrary Dynamical Systems by Wavelet Bases

2001 ◽  
Author(s):  
Roger Ghanem ◽  
Francesco Romeo
Keyword(s):  
Dynamical Systems ◽  
Reduction Process ◽  
Inner Product ◽  
Scaling Functions ◽  
Time Varying ◽  
Governing Equations ◽  
Wavelet Bases ◽  
Input And Output ◽  
Analytical Expressions

Abstract A procedure is developed for the identification and classification of nonlinear and time-varying dynamical systems based on measurements of their input and output. The procedure consists of reducing the governing equations with respect to a basis of scaling functions. Given the localizing properties of wavelets, the reduced system is well adapted to predicting local changes in time as well as changes that are localized to particular components of the system. The reduction process relies on traditional Galerkin techniques and recent analytical expressions for evaluating the inner product between scaling functions and their derivatives. Examples from a variety of dynamical systems are used to demonstrate the scope and limitations of the proposed method.

The Influence of Variable-Speed Waveforms on Vibration Suppression in Time-Varying Speed Cutting

2013 ◽  
Vol 690-693 ◽  
pp. 2514-2518
Author(s):  
Juan Cong ◽  
Yun Wang ◽  
Wei Na Yu
Keyword(s):  
Wave Speed ◽  
Vibration Suppression ◽  
Sine Wave ◽  
Time Varying ◽  
Variable Speed ◽  
Suppression Effect ◽  
Speed Variation ◽  
Input And Output ◽  
System Input ◽  
Better Than

Through the research on the change of system input and output energy in time-varying speed cutting, the influence of variable-speed waveforms on vibration suppression effect in time-varying speed cutting is quantitatively analyzed in this paper. A conclusion can be drawn that sine wave speed variation is better than triangle wave speed variation in vibration suppression.

scholarly journals Prediction-based control of LTI systems with input and output time-varying delays

2018 ◽  
Vol 112 ◽  
pp. 24-30 ◽  
Author(s):  
V. Léchappé ◽  
E. Moulay ◽  
F. Plestan
Keyword(s):  
Time Varying ◽  
Input And Output ◽  
Output Time

A Wavelet Based Procedure to Study Vibrations and Stability

1999 ◽  
Author(s):  
S. Pernot ◽  
C. H. Lamarque
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Time Varying ◽  
Differential Systems ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential

Abstract A Wavelet-Galerkin procedure is introduced in order to obtain periodic solutions of multidegrees-of-freedom dynamical systems with periodic time-varying coefficients. The procedure is then used to study the vibrations of parametrically excited mechanical systems. As problems of stability analysis of nonlinear systems are often reduced after linearization to problems involving linear differential systems with time-varying coefficients, we demonstrate the method provides efficient practical computations of Floquet exponents and consequently allows to give estimators for stability/instability levels. A few academic examples illustrate the relevance of the method.

scholarly journals Strong Li–Yorke Chaos for Time-Varying Discrete Dynamical Systems with A-Coupled-Expansion

2015 ◽  
Vol 25 (13) ◽  
pp. 1550186 ◽  
Author(s):  
Hua Shao ◽  
Yuming Shi ◽  
Hao Zhu
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Strong Sense ◽  
Time Varying ◽  
Transition Matrices ◽  
Complete Metric Spaces ◽  
Compact Subsets

This paper is concerned with strong Li–Yorke chaos induced by [Formula: see text]-coupled-expansion for time-varying (i.e. nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li–Yorke are established via strict coupled-expansions for irreducible transition matrices in bounded and closed subsets of complete metric spaces and in compact subsets of metric spaces, respectively, where their conditions are weaker than those in the existing literature. One example is provided for illustration.

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