LMIs in Control/pages/TDSDC

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The System[edit | edit source]

The problem is to check the stability of the following linear time-delay system on a delay dependent condition


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

For the purpose of the delay dependent system we rewrite the system as

The Data[edit | edit source]

The matrices are known

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

From the given pieces of information, it is clear that the optimization problem only has a solution if there exists a symmetric positive definite matrix
and a scalar such that


This LMI has been derived from the Lyapunov function for the system. It follows that the system is asymptotically stable if

This is obtained by replacing with

Conclusion:[edit | edit source]

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

Implementation[edit | edit source]

The implementation of the above LMI can be seen here


Related LMIs[edit | edit source]

Time Delay systems (Delay Independent Condition)

External Links[edit | edit source]

Return to Main Page:[edit | edit source]