A block bidiangonal form for block companion matrices
نویسندگان
چکیده
منابع مشابه
The polar decomposition of block companion matrices
Let L(λ) = Inλ m + Am−1λm−1 + · · ·+ A1λ + A0 be an n× n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Pm−1 j=1 AjA ∗ j are nonsingular.
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A polynomial matrix G(z) = Izm −∑m−1 i=0 Ciz with complex coefficients is called discrete-time stable if its characteristic values (i.e. the zeros of detG(z) ) are in the unit disc. A corresponding block companion matrix C is used to study discrete-time stability of G(z) . The main tool is the construction of block diagonal solutions P of a discrete-time Lyapunov inequality P−C∗PC 0 .
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1986
ISSN: 0024-3795
DOI: 10.1016/0024-3795(86)90192-8