LMIs in Control/pages/TDSIC

The SystemEdit

The problem is to check the stability of the following linear time-delay system

 

where

 


  is the initial condition
  represents the time-delay
  is a known upper-bound of  

The DataEdit

The matrices   are known

The LMI: The Time-Delay systems (Delay Independent Condition) Edit

From the given pieces of information, it is clear that the optimization problem only has a solution if there exists two symmetric matrices   such that

 

  

This LMI has been derived from the Lyapunov function for the system. By Schur Complement we can see that the above matrix inequality is equivalent to the Riccati inequality
 

Conclusion:Edit

We can now implement these LMIs to do stability analysis for a Time delay system on the delay independent condition

ImplementationEdit

The implementation of the above LMI can be seen here

https://github.com/yashgvd/LMI_wikibooks

Related LMIsEdit

Time Delay systems (Delay Dependent Condition)

External LinksEdit

Return to Main Page:Edit