Jump to content

LMIs in Control/Click here to continue/Optimal control systems/H2-Optimal Observer

From Wikibooks, open books for an open world

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.

Return to Main Page:

[edit | edit source]