LMIs in Control/Discrete-Time Systems/Discrete-Time H2-Optimal Observer
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LMIs in Control/Discrete-Time Systems/Discrete-Time H2-Optimal Observer
The System
[edit | edit source]Where it is assumed that : is detectable.
The Data
[edit | edit source]The matrices .
The Optimization Problem
[edit | edit source]An observer of the form:
is to be designed, where is the observer gain.
Defining the error state , the error dynamics are found to be
,
and the performance output is defined as
.
The observer gain is to be designed such that the of the transfer matrix from to , given by
is minimized.
The LMI: Discrete-Time H2-Optimal Observer
[edit | edit source]The discrete-time -optimal observer gain is synthesized by solving for , , , and that minimize subject to ,
Conclusion:
[edit | edit source]The -optimal observer gain is recovered by and the norm of is .
Implementation
[edit | edit source]Related LMIs
[edit | edit source]Discrete-Time Mixed H2-H∞-Optimal Observer//
Discrete-Time H∞-Optimal Observer//
External Links
[edit | edit source]A list of references documenting and validating the LMI.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.