LMI-based synthesis for controlling periodic solutions in a class of nonlinear systems

2002 ◽  
Author(s):  
M. Basso ◽  
L. Giovanardi ◽  
A. Tesi
Keyword(s):  
Nonlinear Systems ◽  
Periodic Solutions

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 Affine-Periodic Solutions for Dissipative Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yu Zhang ◽  
Xue Yang ◽  
Yong Li
Keyword(s):  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Periodic System ◽  
Dissipative Systems ◽  
Oscillation Mechanism

As generalizations of Yoshizawa’s theorem, it is proved that a dissipative affine-periodic system admits affine-periodic solutions. This result reveals some oscillation mechanism in nonlinear systems.

scholarly journals Periodic Solutions for a System of Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Shugui Kang ◽  
Bao Shi
Keyword(s):  
Nonlinear Systems ◽  
Critical Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Second Order ◽  
System Of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.

A Theory of Index for Point Mapping Dynamical Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 185-190 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Difference Equations ◽  
Vector Fields ◽  
Time Difference ◽  
Point Mapping ◽  
Strongly Nonlinear

Dynamical systems governed by discrete time-difference equations are referred to as point mapping dynamical systems in this paper. Based upon the Poincare´ theory of index for vector fields, a theory of index is established for point mapping dynamical systems. Besides its intrinsic theoretic value, the theory can be used to help search and locate periodic solutions of strongly nonlinear systems.

Sign in / Sign up

Export Citation Format

Share Document