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
editConsider the continuous-time generalized plant with state-space realization
where it is assumed that is detectable.
The Data
editThe matrices needed as input are .
The Optimization Problem
editThe 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
editThe mixed -optimal observer gain is synthesized by solving for , and that minimize subject to ,
Conclusion:
editThe mixed -optimal observer gain is recovered by , the norm of is less than and the norm of T(s) is less than .
Implementation
editLink to the MATLAB code designing - Optimal Observer
External Links
edit- 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
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