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LMIs in Control/pages/Quadratic Polytopic Hinf- Optimal State Feedback Control

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Quadratic Polytopic Full State Feedback Optimal Control

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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 off of performance specifications given. methods formulate this task as an optimization problem and attempt to minimize the norm of the system.

The System

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Consider System with following state-space representation.


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

Add uncertainty to system matrices


New state-space representation


The Optimization Problem:

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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:

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An LMI for Quadratic Polytopic Optimal State-Feedback Control


Conclusion:

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The Optimal State-Feedback Controller is recovered by
Controller will determine the bound on the norm of the system.

Implementation:

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https://github.com/JalpeshBhadra/LMI/tree/master

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Full State Feedback Optimal Controller

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