# LMIs in Control/pages/H2 Optimal Observer

State observer is a system that provides estimates of internal states of a given real system, from measurements of the inputs and outputs of the real system.The goal of -optimal state estimation is to design an observer that minimizes the norm of the closed-loop transfer matrix from w to z. Kalman filter is a form of Optimal Observer.

**The System**[edit | edit source]

Consider the continuous-time generalized plant with state-space realization

**The Data**[edit | edit source]

The matrices needed as input are .

**The Optimization Problem**[edit | edit source]

The task is to design an observer of the following form:

**The LMI:** Optimal Observer[edit | edit source]

LMIs in the variables are given by:

**Conclusion:**[edit | edit source]

The -optimal observer gain is recovered by and the norm of T(s) is

**Implementation**[edit | edit source]

https://github.com/Ricky-10/coding107/blob/master/H2%20Optimal%20Observer

# 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.
- https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.1310