کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6417082 1338528 2015 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Geometric and asymptotic properties associated with linear switched systems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Geometric and asymptotic properties associated with linear switched systems
چکیده انگلیسی

Consider a continuous-time linear switched system on Rn associated with a compact convex set of matrices. When it is irreducible and its largest Lyapunov exponent is zero there always exists a Barabanov norm associated with the system. This paper deals with two types of issues: (a) properties of Barabanov norms such as uniqueness up to homogeneity and strict convexity; (b) asymptotic behavior of the extremal solutions of the linear switched system. Regarding Issue (a), we provide partial answers and propose four related open problems. As for Issue (b), we establish, when n=3, a Poincaré-Bendixson theorem under a regularity assumption on the set of matrices. We then revisit a noteworthy result of N.E. Barabanov describing the asymptotic behavior of linear switched system on R3 associated with a pair of Hurwitz matrices {A,A+bcT}. After pointing out a gap in Barabanov's proof we partially recover his result by alternative arguments.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 259, Issue 11, 5 December 2015, Pages 5582-5616
نویسندگان
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