LMIs in Control/pages/Optimal Output Feedback H2 LMI

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

Optimal Output Feedback LMI[edit | edit source]

Similar to state feedback, output feedback is necessary when information about the output is not known. Often techniques such as Kalman filtering are implemented to tackle this problem. The method below, however, does not use a filtering technique and instead uses a combination of LMI constraints to perform the output feedback as well as find the minimal bound on the norm of the system. is often done using more classical tools such as Riccati equations. More recently LMI techniques have been created to solve problems such as full state feedback or output feedback as seen below.

The System[edit | edit source]

The system is represented using the 9-matrix notation shown below.

where is the state, is the regulated output, is the sensed output, is the exogenous input, and is the actuator input, at any .

The Data[edit | edit source]

, , , , , , , , are known.

The LMI: Optimal Output Feedback Control LMI[edit | edit source]

The following are equivalent.

1) There exists a such that

2) There exists , , , , , , such that

Conclusion:[edit | edit source]

The above LMI determines the the upper bound on the H2 norm. In addition to this the controller can also be recovered.


for any full-rank and such that


Implementation[edit | edit source]

This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/OF_H2.m

Related LMIs[edit | edit source]

Optimal Output Feedback Hinf

External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]