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

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Definition[edit | edit source]

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 .

Circular Region Stability via the Dilation Lemma[edit | edit source]

Consider , , and , where . 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 , where , such that

Moreover, for every that satisfies

and are solutions to

External Links[edit | edit source]