Lyapunov Functions for Almost Sure Exponential Stability

Author(s):  
Hjortur Björnsson ◽  
Sigurdur Freyr Hafstein
2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang

This paper is concerned with stabilization of impulsive stochastic delay differential systems. Based on the Razumikhin techniques and Lyapunov functions, several criteria onpth moment and almost sure exponential stability are established. Our results show that stochastic functional differential systems may be exponentially stabilized by impulses.


1989 ◽  
Vol 111 (4) ◽  
pp. 641-645 ◽  
Author(s):  
Andrzej Olas

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.


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