Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

2015 ◽  
Vol 352 (4) ◽  
pp. 1378-1396 ◽  
Author(s):  
PooGyeon Park ◽  
Won Il Lee ◽  
Seok Young Lee
Keyword(s):  
Time Delay ◽  
Auxiliary Function ◽  
Quadratic Functions ◽  
Integral Inequalities ◽  
Delay Systems ◽  
Time Delay Systems

scholarly journals Generalized Halanay Inequalities with Applications to Generalized Exponential Stability and Boundedness of Time-Delay Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Dehao Ruan ◽  
Yue Liu
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Integral Inequalities ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Generalized Halanay Inequalities ◽  
Generalized Exponential Stability

In this paper, a class of generalized Halanay inequalities is investigated. Under some assumptions, the generalized exponential stability and boundedness are discussed by means of integral inequalities. We do not require the boundedness of the time-varying delays and coefficients. In addition, our results improve some previous works. At last, three examples and simulations are given to illustrate the effectiveness of the main results.

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