Dynamic Problems Researches Of Neutral Systems With Delays

As an important part of dynamics theory, the dynamical properties of neutral systemhave received considerable attention. In this thesis, we concern the key dynamics ofseveral classes of neutral systems. Several relevant problems attracting more and moreattention in this field are discussed in detail, and a series of well-established, systematical,and important results is obtained. They include the stability problem of neutral systemswith delays, the stability problems of Lur’e neutral systems with delays and the problemof finding an ellipsoidal bound of reachable sets for neutral systems with bounded peakdisturbances. This thesis is divided into five parts, including seven chapters.1. The robust stability problem of uncertain neutral system with discrete delay isstudied. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequal-ities (LMIs), which can be easy to check the robust stability of the considered systems.To obtain less conservative stability conditions, an operator is defined to construct theLyapunov functional. Also, the free-weighting matrix approach is employed to further re-duce the entailed conservativeness. Numerical examples are given to indicate significantimprovements over some existing results.2. The robust stability problem of a class of uncertain neutral systems with distribut-ed delays is studied. By using Lyapunov method and linear matrix inequality technolo-gy, new delay-dependent stability criteria are obtained and formulated in terms of linearmatrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab. Anumerical example is given to illustrate our theoretical results.3. The asymptotical stability problem of Lur’e neutral system with discrete delayis studied. By using Lyapunov method, some inequality analysis and free weighting ma-trices are used to drive new delay-dependent stability criteria. A numerical example isprovided to demonstrate the effectiveness of the proposed method.4. The absolute exponential stability problem of Lur’e neutral systems with time-varying delays is studied. By dividing the discrete delay interval into multiple segmentsand choosing proper Lyapunov functional, some delay-dependent exponential stabilitycriteria are obtained and formulated in terms of linear matrix inequalities (LMIs). The partial integration approach and matrix inequality technique are used to reduce the en-tailed conservativeness. Numerical examples are given to indicate significant improve-ments over some existing results.5. The problems of finding an ellipsoidal bound of reachable sets for a class ofneutral systems with bounded peak disturbances are considered. Based on the modifiedaugmented Lyapunov-Krasovskii type functional, we obtain some delay-dependent re-sults expressed in the form of matrix inequalities containing only one non-convex scalar.Furthermore, a modified integral inequality is used to remove the limitation on the varia-tion rate of the delay. Numerical examples are given to indicate significant improvementsover some existing results.