LMIs in Control/pages/TDSIC

The SystemEdit

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




  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


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


The implementation of the above LMI can be seen here


Related LMIsEdit

Time Delay systems (Delay Dependent Condition)

External LinksEdit

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