LMIs in Control/pages/TDSDC

The System The problem is to check the stability of the following linear time-delay system on a delay dependent condition where 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 The matrices are known The LMI: The Time-Delay systems (Delay Dependent Condition) 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 Here 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: We can now implement these LMIs to do stability analysis for a Time delay system on the delay dependent condition Implementation The implementation of the above LMI can be seen here https://github.com/yashgvd/LMI_wikibooks Related LMIs Time Delay systems (Delay Independent 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: