کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602232 1631168 2008 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On nonsingularity of a polytope of matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On nonsingularity of a polytope of matrices
چکیده انگلیسی

The nonsingularity problem of a polytope of real matrices and its relation to the (robust) stability problem is considered. This problem is investigated by using the Bernstein expansion of the determinant function. Here we adapt the known Bernstein algorithm for checking the positivity of a multivariate polynomial on a box to the nonsingularity problem. It is shown that for a family of Z-matrices the positive stability problem is equivalent to the nonsingularity if this family has a stable member. It is established that the stability of the convex hull of real matrices A1, A2, … , Ak is equivalent to the nonsingularity of the convex hull of matrices A1, A2, … , Ak, jI if A1 is stable.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 5–6, 1 September 2008, Pages 1174-1183