LMIs in Control/pages/TDSIC

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The System[edit | edit source]

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 Data[edit | edit source]

The matrices are known

The LMI: The Time-Delay systems (Delay Independent Condition) [edit | edit source]

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 | edit source]

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

Implementation[edit | edit source]

The implementation of the above LMI can be seen here


Related LMIs[edit | edit source]

Time Delay systems (Delay Dependent Condition)

External Links[edit | edit source]

Return to Main Page:[edit | edit source]