Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem

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• 作者：Maria Elena Valcher ; Paolo Santesso
• 关键词：Continuous-time positive system ; Metzler matrix ; Exponential matrix ; Zero pattern ; Directed graph ; Communicating classes ; Frobenius normal form ; Asymptotic exponential cone ; Simplicial cone ; Boundary of a cone
• 刊名：Linear Algebra and its Applications
• 出版年：2010
• 出版时间：1 February 2010
• 年：2010
• 卷：432
• 期：4
• 页码：980-1006
• 全文大小：354 K

文摘

The aim of this paper is that of investigating the asymptotic exponential cone of a single Metzler matrix, introduced in [23], and of defining and analysing the new concept of asymptotic exponential cone of a family of Metzler matrices (along a certain direction). These results will provide necessary and/or sufficient conditions for the solvability of an interesting algebraic problem that arises in the context of continuous-time positive switched systems and, specifically, in the investigation of the reachability property [21,22,25].