LMIs in Control/Discrete-Time Systems/Discrete-Time H2-Optimal Observer

The System Where it is assumed that : is detectable. The Data The matrices . The Optimization Problem An observer of the form: is to be designed, where is the observer gain. Defining the error state , the error dynamics are found to be , and the performance output is defined as . The observer gain is to be designed such that the of the transfer matrix from to , given by is minimized. The LMI: Discrete-Time H2-Optimal Observer The discrete-time -optimal observer gain is synthesized by solving for , , , and that minimize subject to , Conclusion: The -optimal observer gain is recovered by and the norm of is . Implementation https://github.com/rezajamesahmed/LMImatlabcode/blob/master/Discrete_Time_H2_Optimal_Observer_LMIs_Wikibook_Example.m Related LMIs Discrete-Time Mixed H2-H∞-Optimal Observer// Discrete-Time H∞-Optimal Observer// External Links A list of references documenting and validating the LMI. 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. LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd. Return to Main Page: