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.
Consider the continuous-time generalized plant with state-space realization
where it is assumed that is detectable.
The matrices needed as input are .
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
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The mixed -optimal observer gain is synthesized by solving for , and that minimize subject to ,
The mixed -optimal observer gain is recovered by , the norm of is less than and the norm of T(s) is less than .
Link to the MATLAB code designing - Optimal Observer
Code Optimal Observer