LMIs in Control/pages/H2OptimalObserver

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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]

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

The Data[edit]

The matrices needed as input are .

The Optimization Problem[edit]

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

The LMI: Optimal Observer[edit]

LMIs in the variables are given by:


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



External Links[edit]

A list of references documenting and validating the LMI.

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