中立型随机时滞系统的稳定性、H∞-控制及在反应耗散系统中的应用

The topic is mainly concerned with the stability and H∞-control for neutral stochastic systems with time-varying delay and its applications into reaction-diffusion systems. Firstly, in order to overcome the difficulties which come from the presences of the neutral item, time-varying delay, parameters uncertainties and stochastic perturbations, an integral inequality is established for neutral stochastic time-delay systems. And by constructing an appropriate Lyapunov-Krasovskii functional, the exponenital stability for such systems is considered. The obtained delay-dependent sufficient conditions can extend and improve some existing reports. The derived sufficient conditions by using this inequality have three advantages: 1. the decisive variables involved are much fewe;2. the range of their applications is large; 3. the computational complexity needed is simple. Secondly, based on the obtained stability criteria of such systems, the H∞-controller can be designed and the corresponding sufficient conditions are given. Thirdly, after applying the semi-discrete finite difference scheme,the neutral stochastic partial time-delay systems with reaction-diffusion can be written as neutral stochastic time-delay systems by introducing the interpolation operator and using the Kronecker product. And based on the obtained results above, the stability and the H∞-controller design for neutral stochastic partial time-delay systems with reaction-diffusion are well studied and some sufficient conditions are given. The analysis of the effects brought from the time-delay, stochastic perturbation and discretization errors is conducted. Finally, some numerical simulations are provided to show the effectiveness of the obtained results.

本课题主要以中立型随机时滞系统的稳定性、H∞-控制及在反应耗散系统中的应用为研究对象。首先，对中立型随机时滞系统，建立积分不等式，克服中立型、变时滞、系数的不确定性和随机干扰等因素出现带来的困难，构造一合适的李雅普诺夫泛函，开展此系统稳定性的研究，给出一依赖于时滞的充分条件，推广和改进已有的结果。利用积分不等式方法所得到的充分条件有三个优点：1、所需的决策变量少; 2、实用范围广; 3、计算复杂性小。其次，运用所得到的理论结果，研究中立型随机时滞系统的H∞-控制，给出其相应的充分条件。再次，考虑带反应耗散项的中立型随机偏时滞系统的稳定性和H∞-控制，采用半离散有限差分方法，引入内插算子和利用矩阵Kronecker乘积，将所考虑的系统转化为中立型随机时滞系统，再基于上述方法进行研究，给出其充分条件,分析时滞、随机干扰和离散误差对所得到的结果的影响。最后，利用数值实例验证所得到结果的有效性。

本课题主要是以中立型随机时滞系统的稳定性分析及相关控制问题为主要研究对象。中立型随机时滞系统在化学反应耗散过程、大规模的集成电路系统、Lotka-Volterra系统、带质点-弹簧-钟摆的力学模型等问题中有较强的应用。. 主要研究内容、重要结果和关键数据:.1. 为了克服中立项、随机干扰和变时滞等因素同时带来的困难, 建立积分不等式, 讨论带变时滞的中立型随机系统的矩指数稳定性与H_{\infty}-控制, 其结果发表在《IET-Control Theory and Applications》、《Digital Signal Processing》、《Applied Mathematics and Computation》和《IET-Signal Processing》等SCI杂志上。.2. 为了克服中立型、随机干扰和变时滞等因素同时带来的困难, 在不要求对变时滞函数添加导数小于1的限制性条件下, 建立时滞积分不等式, 研究带马尔可夫跳的中立型随机变时滞系统的矩指数稳定性、几乎必然指数稳定性和自适应反馈控制等问题, 其结果发表在SCI杂志《IEEE Transactions on Cybernetics》、《IEEE Transactions on Neural Networks and Learning Systems》、《Systems & Control Letters》、《International Journal of Robust and Nonlinear Control》和《IEEE Transactions on Automatic Control》等SCI杂志上。. 科学意义:.1. 此课题为研究中立型随机复杂时滞网络的矩指数稳定型同步、几乎必然指数型同步和自适应反馈控制等问题打下基础。目前, 部分结果发表在SCI杂志《IEEE Transactions on Neural Networks and Learning Systems》上。.2. 此课题为研究中立型随机变时滞系统的矩指数稳定性及相关控制, 且得到与时滞依赖鲁棒控制条件在理论研究方法上打下基础。.3. 此课题为研究中立型随机复杂时滞网络的脉冲控制、Pinng反馈控制和自适应控制等问题找到理论研究方法。.4. 此课题为研究中立型随机时滞系统的动力学性质提供新的研究方法。