A sufficient condition for the uniform exponential stability of time-varying systems with noise

2004 ◽  
Vol 56 (7) ◽  
pp. 951-960 ◽  
Author(s):  
G. Grammel ◽  
I. Maizurna
Keyword(s):  
Exponential Stability ◽  
Sufficient Condition ◽  
Time Varying ◽  
Uniform Exponential Stability ◽  
Time Varying Systems

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

The uniform exponential stability of a class of linear differential–difference equations in a Hilbert space

1981 ◽  
Vol 89 (3-4) ◽  
pp. 201-215 ◽  
Author(s):  
Richard Datko
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Exponential Stability ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Exponential Stability ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is given for the uniform exponential stability of certain autonomous differential–difference equations whose phase space is a Hilbert space. It is shown that this property is preserved when the delays depend homogeneously on a nonnegative parameter.

scholarly journals Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

2012 ◽  
Vol 17 (2) ◽  
pp. 210-222 ◽  
Author(s):  
Xiu Liu ◽  
Shouming Zhong ◽  
Xiuyong Ding
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Functionals ◽  
Sufficient Condition ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Numerical Example ◽  
Impulsive Switched Systems ◽  
Theoretical Results

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

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