LMIs in Control/Click here to continue/LMIs in system and stability Theory/Quadratic Hurwitz Stabilization for Polytopic Systems

This section studies the Quadratic Hurwitz stabilization for polytopic systems.

The System edit

Given a state-space representation of a linear system

 

 

 

 

 

(1)

LMI Condition edit

With   , the quadratic Hurwitz Stabilization problem has a solution if and only if there exists a symmetric positive definite matrix   and a matrix   satisfying the below LMI :

 

 

 

 

 

(2)

In this case, a solution to the problem is given by

 

 

 

 

 

(3)

Conclusion edit

Stability of a system does not guarantee quadratic stability. Since quadratic stability can represent infinite LMI constraints, it is not tractable. Therefore, to make it feasible and tractable, polytopic sets are helpful.

External Links edit