scholarly journals A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

2012 ◽  
Vol 7 (1) ◽  
pp. 8 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Output Feedback ◽  
Feedback Controller ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Output Feedback Controller ◽  
Fuzzy Dynamical Systems

Non-Stationary Oscillations at Slow Transitions Across Instabilities

2007 ◽  
Author(s):  
Rudolf R. Pusˇenjak ◽  
Maks M. Oblak ◽  
Jurij Avsec
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Time Scales ◽  
Primary Resonance ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Excitation Parameter ◽  
Linear Dynamical Systems ◽  
Weakly Nonlinear ◽  
Non Linear

The paper presents the study of non-stationary oscillations, which is based on extension of Lindstedt-Poincare (EL-P) method with multiple time scales for non-linear dynamical systems with cubic non-linearities. The generalization of the method is presented to discover the passage of weakly nonlinear systems through the resonance as a control or excitation parameter varies slowly across points of instabilities corresponding to the appearance of bifurcations. The method is applied to obtain non-stationary resonance curves of transition across points of instabilities during the passage through primary resonance of harmonically excited oscillators of Duffing type.

Extended Lindstedt-Poincare Method With Multiple Time Scales for Nonstationary Oscillations

2006 ◽  
Author(s):  
Rudi R. Pusenjak ◽  
Jurij Avsec ◽  
Maks M. Oblak
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Multiple Scales ◽  
Duffing Oscillator ◽  
Excitation Frequency ◽  
Van Der Pol Oscillator ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Response Curves ◽  
Nonstationary Oscillations

The paper presents the extended Lindstedt-Poincare (ELP) method, which applies multiple time scales to treat nonstationary oscillations arising in dynamical systems with cubic non-linearities. The passage through the resonance is conducted to study deviations from the stationary response. The method is applied to the dynamical systems such as Duffing oscillator and van der Pol oscillator, whereat effects of varying the excitation frequency and varying the excitation amplitudes, respectively are studied. It is shown that application of multiple scales benefits to find more accurate expressions of stationary responses in comparison to the conventional Lindstedt-Poincare method and consequently contributes to the versatile and effective calculation of the nonstationary frequency response curves.

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