On Stability of Time-Varying Multidimensional Linear Systems

1999 ◽  
Vol 121 (4) ◽  
pp. 509-511 ◽  
Author(s):  
Jinn-Wen Wu ◽  
Rong-Fong Fung
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Stiffness Matrix ◽  
Minimum Amount ◽  
Sufficient Condition ◽  
Time Varying ◽  
Multidimensional Linear

In this Technical Brief, a sufficient condition to guarantee the exponential stability for a time-varying system X¨ + DX˙ + K(t)X = 0 is obtained. We mainly made up the condition by estimating the minimum amount of the damping to cope with a time-varying stiffness matrix K(t).

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.

Exponential Stability for Grey Linear Systems with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 2258-2262
Author(s):  
Ji Chao Wang ◽  
Li Jun Song ◽  
Wei Liu ◽  
Jin Fang Han
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Stability Problem ◽  
Measure Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Matrix Measure ◽  
Time Varying Delay ◽  
The Matrix ◽  
Varying Delay

In this paper, the exponential stability problem of grey linear systems with time-varying delay is investigated. By using the matrix measure theory and differential inequality approach, some practical sufficient conditions for guaranteeing the exponential stability of the grey linear systems with time-varying delay are presented. The grey-matrix measure and norm are also introduced.

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