LMIs in Control/pages/quadratic polytopic h2 optimal state feedback control

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LMIs in Control/pages/quadratic polytopic h2 optimal state feedback control

Quadratic Polytopic Full State Feedback Optimal Control[edit | edit source]

For a system having polytopic uncertainties, Full State Feedback is a control technique that attempts to place the system's closed-loop system poles in specified locations based on performance specifications given, such as requiring stability or bounding the overshoot of the output. By minimizing the norm of this system we are minimizing the effect noise has on the system as part of the performance specifications.

The System[edit | edit source]

Consider System with following state-space representation.

where , , , , , , , , , , , , , for any .

Add uncertainty to system matrices

New state-space representation

The Data[edit | edit source]

The matrices necessary for this LMI are

The Optimization Problem:[edit | edit source]

Recall the closed-loop in state feedback is:

This problem can be formulated as optimal state-feedback, where K is a controller gain matrix.

The LMI: An LMI for Quadratic Polytopic Optimal[edit | edit source]

State-Feedback Control

Conclusion:[edit | edit source]

The Optimal State-Feedback Controller is recovered by

Implementation:[edit | edit source]


Related LMIs[edit | edit source]

Optimal State-Feedback Controller

External Links [edit | edit source]