LMIs in Control/pages/TDSIC

The System 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 Data The matrices are known The LMI: The Time-Delay systems (Delay Independent Condition) 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: We can now implement these LMIs to do stability analysis for a Time delay system on the delay independent condition Implementation The implementation of the above LMI can be seen here https://github.com/yashgvd/LMI_wikibooks Related LMIs Time Delay systems (Delay Dependent Condition) External Links - 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. Return to Main Page: