LMIs in Control/Click here to continue/Observer synthesis/Full-order Hinf state Observer
In this section, we design full order H- state observer.
The System edit
Given a state-space representation of a linear system
- are the state vector, measured output vector and output vectors of interest.
- are the disturbance vector and control vector respectively.
The Data edit
are system matrices
Definition edit
For the system , a full order state observer of the form of equation (1) is introduced and the estimate of interested output is given by .
-
(
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The estimate of interested output is
-
(
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Given the system and a positive scalar , L is found such that
-
(
)
LMI Condition edit
The state observers problem has a solution if and only if there exists a symmetric positive definite matrix and a matrix satisfying the below LMI
-
(
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When such a pair of matrics is found, the solution is
-
(
)
Implementation edit
This implementation requires Yalmip and Mosek.
Conclusion edit
Thus, an state observer is designed such that the output vectors of interest are accurately estimated.
External Links edit
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & Francis Group, 2013