Simple uniform exponential stability conditions for a system of linear delay differential equations
2014; Elsevier BV; Volume: 250; Linguagem: Inglês
10.1016/j.amc.2014.10.117
ISSN1873-5649
AutoresLeonid Berezansky, Josef Diblı́k, Zdeněk Svoboda, Zdeněk Šmarda,
Tópico(s)Numerical methods for differential equations
ResumoUniform exponential stability of linear systems with time varying coefficientsẋi(t)=-∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,…,mis studied, where t⩾0,m and rij,i,j=1,…,m are natural numbers, aijk:[0,∞)→R and hijk:[0,∞)→R are measurable functions. New explicit result is derived with the proof based on Bohl–Perron theorem. The resulting criterion has advantages over some previous ones in that, e.g., it involves no M-matrix to establish stability. Several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results.
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