کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602804 1631182 2006 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Generalized matrix diagonal stability and linear dynamical systems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Generalized matrix diagonal stability and linear dynamical systems
چکیده انگلیسی

Let A = (aij) be a real square matrix and 1 ⩽ p ⩽ ∞. We present two analogous developments. One for Schur stability and the discrete-time dynamical system x(t + 1) = Ax(t), and the other for Hurwitz stability and the continuous-time dynamical system . Here is a description of the latter development.For A, we define and study “Hurwitz diagonal stability with respect to p-norms”, abbreviated “HDSp”. HDS2 is the usual concept of diagonal stability. A is HDSp implies “Re λ < 0 for every eigenvalue λ of A”, which means A is “Hurwitz stable”, abbreviated “HS”. When the off-diagonal elements of A are nonnegative, A is HS iff A is HDSp for all p.For the dynamical system , we define “diagonally invariant exponential stability relative to the p-norm”, abbreviated DIESp, meaning there exist time-dependent sets, which decrease exponentially and are invariant with respect to the system. We show that DIESp is a special type of exponential stability and the dynamical system has this property iff A is HDSp.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 419, Issues 2–3, 1 December 2006, Pages 299-310