| The neutral Markov jump system is an important part of dynamics system-s,and the dynamical properties of neutral Markov jump system have been one of the focuses of scholars both at home and abroad.In this thesis,several relevant problems are discussed in detail,and a series of well-established results is obtained.They in-clude the stability of neutral Markov jumping systems with discrete time delays,the time-limited stability of neutral Markov jumping systems with discrete time delays and the reachable set ellipsoid boundary of neutral Markov jumping systems with discrete time.This thesis is divided into three parts,including five chaptersFirstly,the stability of neutral Markov jumping system with discrete time delay is studied.By constructing appropriate Lyapunov functional,some matrix inequality analysis and free weighting matrices are used to drive new stability criteria.These conditions are obtained and formulated in terms of linear matrix inequalities which can be solved by LMI toolbox in MATLAB.Numerical examples are given to indicate the effectiveness of the proposed methodSecondly,the finite-time stability of neutral Markov jumping systems with dis-crete time delays is studied.By using Lyapunov method and linear matrix inequality technology,new finite-time stability criteria are obtained.Furthermore,a modified in-tegral inequality and the Gronwall inequality are used To drive less conservative finite-time stability conditions.A numerical example is given to illustrate our theoretical results.Finally,the problem of finding an ellipsoidal bound of reachable sets for neutral Markov jump system with discrete time delay is studied.Based on the modified Lya-punov functional,we obtain some delay-dependent results expressed in the form of matrix inequalities,which can be solved by LMI toolbox in MATLAB.Furthermore,a modified integral inequality is used to remove the limitation on the variation rate of the delay.Two examples are given to indicate the effectiveness of the proposed method. |
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