LMIs in Control/pages/HInf Optimal Filter
< LMIs in Control | pages
(Redirected from 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 Data edit
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 filter edit
Solve for , and that minimize subject to .
Conclusion: edit
The filter is recovered by and .
Implementation edit
External links edit
- [1]- Optimal Filtering
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.