LMIs in Control/pages/H-infinity filtering
This is a WIP based on the template.
For the application of this LMI, we will look at linear systems that can be represented in state space as
where represent the state vector, the measured output vector, and the output vector of interest, respectively, is the disturbance vector, and and are the system matrices of appropriate dimension.
The data are (the disturbance vector), and and (the system matrices). Furthermore, the matrix is assumed to be stable
The Optimization Problem
We need to design a filter that will eliminate the effects of the disturbances as best we can. For this, we take a filter of the following form:
where is the state vector, is the estimation vector of z, and are the coefficient matrices of appropriate dimensions.
Note that the combined complete system can be represented as
where is the estimation error,
is the state vector of the system, and are the coefficient matrices, defined as:
In other words, for the system defined above we need to find such that
where is a positive constant, and
The LMI: H-inf Filtering
The solution can be obtained by finding matrices that obey the following LMIs:
To find the corresponding filter, use the optimized matrices from the solution to find:
These matrices can then be used to produce to construct the filter described above, that will best eliminate the disturbances of the system.
A link to CodeOcean or other online implementation of the LMI
Links to other closely-related LMIs
A list of references documenting and validating the LMI.
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