LMIs in Control/Observer Synthesis/Continuous Time/Full-Order H-infinity State Observer
In this section, we design full order H- state observer.
The System
[edit | edit source]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 | edit source]are system matrices
Definition
[edit | edit source]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 .
-
()
The estimate of interested output is
-
()
Given the system and a positive scalar , L is found such that
-
()
LMI Condition
[edit | edit source]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
-
()
When such a pair of matrics is found, the solution is
-
()
Implementation
[edit | edit source]This implementation requires Yalmip and Mosek.
Conclusion
[edit | edit source]Thus, an state observer is designed such that the output vectors of interest are accurately estimated.
External Links
[edit | edit source]- 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