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.
Consider the continuous-time generalized plant with state-space realization
The matrices needed as input are .
The Optimization ProblemEdit
The task is to design an observer of the following form:
The LMI: Optimal ObserverEdit
LMIs in the variables are given by:
The -optimal observer gain is recovered by and the norm of T(s) is
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.