LMIs in Control/pages/MixedH2HinfinityOptimalobserver

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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[edit]

Consider the continuous-time generalized plant with state-space realization

where it is assumed that is detectable.

The Data[edit]

The matrices needed as input are .

The Optimization Problem[edit]

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[edit]

The mixed -optimal observer gain is synthesized by solving for , and that minimize subject to ,


Conclusion:[edit]

The mixed -optimal observer gain is recovered by , the norm of is less than and the norm of T(s) is less than .

Implementation[edit]

Link to the MATLAB code designing - Optimal Observer

Code Optimal Observer


External Links[edit]

Related LMIs[edit]


Return to Main Page:[edit]