Linear Matrix Inequality

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A Linear Matrix Inequality is a constraint equation of the form [math]\displaystyle{ LMI(u) := F_0 + u_1F_1 + … + u_qF_q \preceq 0 }[/math] where ...



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/linear_matrix_inequality Retrieved:2015-6-7.
    • In convex optimization, a linear matrix inequality (LMI) is an expression of the form : [math]\displaystyle{ \operatorname{LMI}(y):=A_0+y_1A_1+y_2A_2+\cdots+y_m A_m\geq0\, }[/math] where
      • [math]\displaystyle{ y=[y_i\,,~i\!=\!1,\dots, m] }[/math] is a real vector,
      • [math]\displaystyle{ A_0, A_1, A_2,\dots,A_m }[/math] are [math]\displaystyle{ n\times n }[/math] symmetric matrices [math]\displaystyle{ \mathbb{S}^n }[/math] ,
      • [math]\displaystyle{ B\geq0 }[/math] is a generalized inequality meaning [math]\displaystyle{ B }[/math] is a positive semidefinite matrix belonging to the positive semidefinite cone [math]\displaystyle{ \mathbb{S}_+ }[/math] in the subspace of symmetric matrices [math]\displaystyle{ \mathbb{S} }[/math] .
    • This linear matrix inequality specifies a convex constraint on y.

2004