LMIs in Control/pages/discrete time mixed h2 hinf optimal observer

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LMIs in Control/pages/discrete time mixed h2 hinf optimal observer

The System[edit]

Where it is assumed that : is detectable.

The Data[edit]

The matrices .

The Optimization Problem[edit]

An observer of the form:

is to be designed, where is the observer gain.

Defining the error state , the error dynamics are found to be

,

and the performance output is defined as

.

The observer gain is to be designed to minimize the norm of the closed loop transfer matrix from the exogenous input to the performance output is less than , where

The LMI: Discrete-Time Mixed H2-Hinf-Optimal Observer[edit]

The discrete-time mixed--optimal observer gain is synthesized by solving for , , , and that minimize J subject to ,

Conclusion:[edit]

The mixed--optimal observer gain is recovered by , the norm of is less than , and the norm of is less than .

Implementation[edit]

WIP! NEEDS TO BE UPDATED: THE CURRENTLY LINKED CODE IS FOR DISCRETE TIME H2 OPTIMAL OBSERVER: https://github.com/rezajamesahmed/LMImatlabcode/blob/master/Discrete_Time_H2_Optimal_Observer_LMIs_Wikibook_Example.m

Related LMIs[edit]

Discrete-Time Mixed H2-H∞-Optimal Observer//

Discrete-Time H∞-Optimal Observer//

External Links[edit]

A list of references documenting and validating the LMI.


Return to Main Page:[edit]