LMIs in Control/Click here to continue/LMIs in system and stability Theory/Conic Sector Region Stability via the Dilation Lemma

Definition edit

Consider  . The matrix   is  -stable if and only if there exists  , where  , such that

 ,

or equivalent

 ,

where   is the Kroenecker product,

The eigenvalues of a  -stable matrix lie within the LMI region  , which is defined as

 , where

 ,

 ,  , and   is the complex conjugate of  .

Conic Sector Region Stability via the Dilation Lemma edit

Consider   and  .

The matrix   satisfies  , where  , if and only if there exist   and  , where  , such that

 .

Equivalently, the matrix   satisfies   if and only if there exist   and  , and  , where  , such that

 .

Moreover, for every   that satisfies

 ,

  and   are solutions to

 


External Links edit