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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

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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 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

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Consider System with following state-space representation.


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


Add uncertainty to system matrices


New state-space representation


The Data

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The matrices necessary for this LMI are

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: An LMI for Quadratic Polytopic Optimal

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State-Feedback Control



Conclusion:

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The Optimal State-Feedback Controller is recovered by


Implementation:

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https://github.com/JalpeshBhadra/LMI/blob/master/H2_optimal_statefeedback_controller.m

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Optimal State-Feedback Controller

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