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LMIs in Control/pages/Hinfinityoptimalfilter
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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:
Consider the continuous-time generalized LTI plant with minimal states-space realization
where it is assumed that is Hurwitz.
The Data
The matrices needed as inputs are .
The Optimization Problem:
An -optimal filter is designed to minimize the norm of in following equation.
The LMI: - Optimal filter
Solve for , and that minimize subject to .
Conclusion:
The filter is recovered by and .
Implementation
https://github.com/Ricky-10/coding107/blob/master/Hinfinity%20Optimal%20filter- - Optimal Filter
External links
- Optimal Filtering
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.