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

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

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 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:[edit | edit source]

An LMI for Quadratic Polytopic Optimal State-Feedback Control

Conclusion:[edit | edit source]

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

Implementation:[edit | edit source]


Related LMIs[edit | edit source]

Full State Feedback Optimal Controller

External Links [edit | edit source]