scholarly journals Stability analysis based on monodromy matrix for switched dynamical systems

2021 ◽  
Vol 12 (3) ◽  
pp. 237-256
Author(s):  
Hiroyuki Asahara ◽  
Takuji Kousaka
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Monodromy Matrix

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Stability analysis of flame fronts: Dynamical systems approach in the complex plane

1999 ◽  
Vol 59 (3) ◽  
pp. 2587-2593 ◽  
Author(s):  
Oleg Kupervasser ◽  
Zeev Olami ◽  
Itamar Procaccia
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Complex Plane ◽  
Systems Approach

Stability analysis of discontinuous dynamical systems determined by semigroups

2005 ◽  
Vol 50 (9) ◽  
pp. 1277-1290 ◽  
Author(s):  
A.N. Michel ◽  
Ye Sun ◽  
A.P. Molchanov
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems

Stability analysis of dynamical systems via R-functions

2009 ◽  
Author(s):  
A. Balestrino ◽  
A. Caiti ◽  
E. Crisostomi ◽  
S. Grammatico
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
R Functions

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.

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