非线性与时滞随机系统的稳定性分析及镇定方法研究

项目名称： 非线性与时滞随机系统的稳定性分析及镇定方法研究

项目编号： No.61273126

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 邓飞其

作者单位： 华南理工大学

项目金额： 82万元

中文摘要： 在任何实际系统及其外部环境中都存在着随机因素，影响系统的动态。实际上，随机模型有时更能准确反映自然与社会工程系统动态特性。含有非线性、时滞、变系数、Markov跳变、脉冲、分布参数、奇异性、模糊性等复杂因素的随机系统的控制理论是当前的研究热点。本项目以非线性、时滞随机系统为研究对象，探讨系统的稳定性与镇定问题。以体现随机系统特色、减小稳定性判据的保守性为追求目标，在非线性与时滞随机系统稳定性分析方法、镇定、噪声镇定等方面探索新的方法与途径。主要探索非线性随机系统稳定性的矩方程法、时滞随机系统稳定性分析的Lyapunov函数法+系统方程法；建立具有随机系统特色的Lyapunov稳定性定理、新型Razumikhin定理、时滞随机系统的算子型稳定性定理等，为非线性与时滞随机系统稳定性分析、镇定控制这一经典问题带来一些新的视野和理论方法，进一步完善和发展随机系统理论，为工程和社会实践提供理论依据。

中文关键词： 非线性随机系统；时滞；稳定性分析；镇定；控制

英文摘要： There always exist random factors in the real systems and their external environments, which influence the dynamical behavior of the systems. In fact, sometimes, random models can accurately reflect the dynamical characteristics of natural, social and engineering systems. At the time being, the control theory for stochastic systems with various complicated factors such as nonlinearities, time-delays, varying coefficients, Markov jumps, impulses, distributed parameters and fuzziness are the current research hotspots. By this project, the stability and stabilization will be investigated for the nonlinear or delayed stochastic systems. Novel methods and approaches for the stability analysis, stabilization and stabilization by noise will be developed in order that less conservativeness and more features on randomness are implied by the stability criteria obtained. The methods for stability analysis by moment equations for nonlinear stochastic systems and those for stability analysis by Lyapunov functions combined with the system equations for the delayed stochastic systems will be mainly explored, and the Lyapunov stability theorem with more features on randomness, new type Razumikhin theorem and the operator approach for the stability theorem of delayed stochastic systems will be also established. We will bring som

英文关键词： Nonlinear Stochastic Systems；Time delayed；Stability Analysis；Stabilization；Control