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 SystemEdit

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

 

where it is assumed that   is detectable.

The DataEdit

The matrices needed as input are  .

The Optimization ProblemEdit

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 ObserverEdit

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  .

ImplementationEdit

Link to the MATLAB code designing  - Optimal Observer

Code   Optimal Observer


External LinksEdit

Related LMIsEdit


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