LMIs in Control/pages/Mixed H2 HInf Optimal Observer

The goal of mixed -optimal state estimation is to design an observer that minimizes the norm of the closed-loop transfer matrix from to , while ensuring that the norm of the closed-loop transfer matrix from to is below a specified bound. The System Consider the continuous-time generalized plant with state-space realization where it is assumed that is detectable. The Data The matrices needed as input are . The Optimization Problem The observer gain L is to be designed to minimize the norm of the closed-loop transfer matrix from the exogenous input to the performance output while ensuring the norm of the closed-loop transfer matrix from the exogenous input to the performance output is less than , where is minimized. The form of the observer would be: is to be designed, where is the observer gain. The LMI: Optimal Observer The mixed -optimal observer gain is synthesized by solving for , and that minimize subject to , Conclusion: The mixed -optimal observer gain is recovered by , the norm of is less than and the norm of T(s) is less than . Implementation Link to the MATLAB code designing - Optimal Observer Code Optimal Observer External Links 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. Related LMIs Optimal observer Optimal observer Return to Main Page: