LMIs in Control/pages/Optimal Output Feedback Hinf LMI

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Optimal Output Feedback LMI[edit | edit source]

Optimal output feedback control is a problem which arises from not knowing all information about the output of the system. It correlates to the state feedback situation where the part of the state is unknown. This issue can arise in decentralized control problems, for example, and requires the use of an "observer-like" solution. One such method is the use of a Kalman Filter, a more classical technique. However, other methods exist that do not implement a Kalman Filter such as the one below which uses an LMI to preform the output feeback. The control methods form an optimization problem which attempts to minimize the norm of the system.

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 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_Hinf.m

Related LMIs[edit | edit source]

Optimal Output Feedback H2

External Links[edit | edit source]

Return to Main Page:[edit | edit source]