Schur stability of convex combination of matrices
نویسندگان
چکیده
منابع مشابه
Singular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
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for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...
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This note considers the stability of uncertain matrices. It is shown that under certain structural assumptions on the uncertain matrices the Schur stability can be assured from computing the numerical radius of the vertex matrices. This result is less conservative than that of using a simultaneous Lyapunov function method. Necessary and sufficient conditions are also obtained for the stability ...
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1 Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia 2 Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia 3 Abdus Salam School of Mathematical Sciences, 68-B, New Muslim Town, Lahore 54600, Pakistan 4 Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90290-s