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

Quadratic Polytopic Full State Feedback Optimal ControlEdit

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 SystemEdit

Consider System with following state-space representation.

 

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

Add uncertainty to system matrices

 

New state-space representation

 

The Optimization Problem:Edit

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

An LMI for Quadratic Polytopic   Optimal State-Feedback Control  
 

 


Conclusion:Edit

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

Implementation:Edit

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

Related LMIsEdit

Full State Feedback Optimal   Controller

External Links Edit