Smooth Lyapunov functions and robustness of stability for difference inclusions

2004 ◽  
Vol 52 (5) ◽  
pp. 395-405 ◽  
Author(s):  
Christopher M Kellett ◽  
Andrew R Teel
Keyword(s):  
Lyapunov Functions ◽  
Difference Inclusions

scholarly journals Stability of differential inclusions: A computational approach

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Vadim Azhmyakov
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Differential Inclusions ◽  
Auxiliary Problem ◽  
Saddle Points ◽  
Computational Approach ◽  
Saddle Point Problems ◽  
Difference Inclusions ◽  
Type Algorithm ◽  
Gradient Type

We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples.

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