A novel integral inequality and its application to stability analysis of linear system with multiple time delays

2022 ◽  
Vol 124 ◽  
pp. 107648
Author(s):  
Li Jin ◽  
Yong He ◽  
Lin Jiang
Keyword(s):  
Stability Analysis ◽  
Linear System ◽  
Integral Inequality ◽  
Time Delays ◽  
Multiple Time ◽  
Multiple Time Delays

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

scholarly journals D-Stability Analysis for a Class of Uncertain Discrete Systems with Multiple Time Delays.

2002 ◽  
Vol 45 (2) ◽  
pp. 601-605 ◽  
Author(s):  
Ching-Fa CHEN ◽  
Shing-Tai PAN ◽  
Jer-Guang HSIEH
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Discrete Systems ◽  
Multiple Time ◽  
Multiple Time Delays
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