Stability Analysis For Neutral Delay Systems

Considerable efforts are concentrated on the development for dynamic systems including time delays, since the delay phenomenon is often encountered in various systems, and is frequently a source of instability. Neutral delay systems not only depend on state delays but also depend on their derivatives, which is more difficult for neutral delay systems to be stabilized. Recently, a great number of stability results for neutral delay system have been reported. In this dissertation, the problem of stability for neutral delay systems based on LMI are deeply investigated and analyzed on the ground of the summarization of the popular methods.First, basic knowledge on neutral delay systems is introduced, including the existence of its solution, property of its eigenvalue equation and Razumikhin theorem.Next, based on the basic knowledge of neutral delay systems, the problem of exponential stability of linear neutral delay systems is studied . A new delay–dep -endent sufficient condition for exponential stability is formulated in terms of linear matrix inequalities (LMIs).Finally, two numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.