LMIs in Control/pages/TDSIC
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]
-  - LMI in Control Systems Analysis, Design and Applications
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- D. d. S. Madeira and J. Adamy, "Static output feedback: An LMI condition for stabilizability based on passivity indices," 2016 IEEE Conference on Control Applications (CCA), Buenos Aires, 2016, pp. 960-965.