LMIs in Control/Click here to continue/LMIs in system and stability Theory/alpha-Region 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 .
α-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 , where , such that
.
Moreover, for every that satisfies
and are solutions to
.
External Links edit
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.