LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Dualization Lemma

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Dualization Lemma[edit | edit source]

Consider and the subspaces , where is invertible and . The following are equivalent.

for all \ and for all .

for all \ and for all .

Example[edit | edit source]

Consider the matrices where which define the quadratic matrix inequality

Define where . Notice that is equivalent to for all \.Additionally, for all is euaivalent to

which is satisfied based on the definition of . By the dualization lemma, is satisfied with if and only if

where , and .

External Links[edit | edit source]