<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHAEL GIL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ABSOLUTE AND INPUT-TO-STATE STABILITIES OF NONAUTONOMOUS SYSTEMS WITH CAUSAL MAPPINGS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword><keyword><style  face="normal" font="default" size="100%">93D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/43-DSA-210.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider systems governed by the scalar equation Xn k=0 ak(t)x (n−k) (t) = [Fx](t) (t ≥ 0), where a0 ≡ 1; ak(t) (k = 1, . . ., n) are positive continuous functions and F is a causal mapping. We also consider the case when F depends on the input. Such equations include differential, integrodifferential and other traditional equations. It is assumed that all the roots rk(t) (k = 1, . . ., n) of the polynomial z n + a1(t)z n−1 + · · · + an(t) are real and negative for all t ≥ 0. Exact explicit conditions for the absolute and input-to-state stabilities of the considered systems are established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">655</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. I. GIL’</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">L2  -STABILITY OF VECTOR EQUATIONS WITH NONLINEAR CAUSAL MAPPINGS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword><keyword><style  face="normal" font="default" size="100%">93D05</style></keyword><keyword><style  face="normal" font="default" size="100%">93D25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-201-220.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L&lt;sup&gt;2&lt;/sup&gt; -norm of solutions are established. The obtained estimates give us explicit conditions for the L&lt;sup&gt;2&lt;/sup&gt; -stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">201</style></section></record></records></xml>