LMIs in Control/pages/Hinfinityoptimalfilter

Optimal filtering is a means of adaptive extraction of a weak desired signal in the presence of noise and interfering signals. The goal of optimal filtering is to design a filter that acts on the output of the generalized plant and optimizes the transfer matrix from w to the filtered output.

The System:Edit

Consider the continuous-time generalized LTI plant with minimal states-space realization

 

where it is assumed that   is Hurwitz.

The DataEdit

The matrices needed as inputs are  .

The Optimization Problem:Edit

An  -optimal filter is designed to minimize the   norm of   in following equation.

 


The LMI: - Optimal filterEdit

Solve for  ,   and   that minimize   subject to  .

 


Conclusion:Edit

The filter is recovered by   and  .

ImplementationEdit

External linksEdit