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

LMIs in Control/pages/quadratic polytopic h2 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 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 SystemEdit

Consider System with following state-space representation.

 

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


Add uncertainty to system matrices

 

New state-space representation

 

The DataEdit

The matrices necessary for this LMI are

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: An LMI for Quadratic Polytopic OptimalEdit

State-Feedback Control
 
 

 
 
 


Conclusion:Edit

The   Optimal State-Feedback Controller is recovered by  


Implementation:Edit

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

Related LMIsEdit

  Optimal State-Feedback Controller

External Links Edit