LMIs in Control/pages/H2 Optimal Observer

From Wikibooks, open books for an open world
Jump to navigation Jump to search

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]


External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]