DOAJ Open Access 2016

New exponential stability conditions for linear delayed systems of differential equations

Leonid Berezansky Josef Diblik Zdenek Svoboda Zdenek Smarda

Abstrak

New explicit results on exponential stability, improving recently published results by the authors, are derived for linear delayed systems $$ \dot{x}_i(t)=-\sum_{j=1}^m \sum_{k=1}^{r_{ij}}a_{ij}^{k}(t)x_j(h_{ij}^{k}(t)),\qquad i=1,\dots,m $$ where $t\ge 0$, $m$ and $r_{ij}$, $i,j=1,\dots,m$ are natural numbers, $a_{ij}^{k}\colon [0,\infty)\to\mathbb{R}$ are measurable coefficients, and $h_{ij}^{k}\colon [0,\infty)\to\mathbb{R}$ are measurable delays. The progress was achieved by using a new technique making it possible to replace the constant $1$ by the constant $1+{1}/{\mathrm{e}}$ on the right-hand sides of crucial inequalities ensuring exponential stability.

Topik & Kata Kunci

Mathematics

Penulis (4)

Leonid Berezansky

Josef Diblik

Zdenek Svoboda

Zdenek Smarda

Format Sitasi

APA MLA BibTeX

Berezansky, L., Diblik, J., Svoboda, Z., Smarda, Z. (2016). New exponential stability conditions for linear delayed systems of differential equations. https://doi.org/10.14232/ejqtde.2016.8.5

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Informasi Jurnal

Tahun Terbit: 2016
Sumber Database: DOAJ
DOI: 10.14232/ejqtde.2016.8.5
Akses: Open Access ✓