【作者】 陈红刚；

【导师】 陈东彦；

【作者基本信息】 哈尔滨理工大学 ， 应用数学， 2008， 硕士

【摘要】 在对实际控制系统建模时,由于不可避免地存在着测量误差、各种干扰以及未建模动态等,导致系统模型与实际问题之间存在着误差,一般称这些误差为系统的不确定性。除此之外,系统中还常常存在着时滞,时滞不仅存在于状态中,而且还可能存在于状态的变化率中,这就是中立型时滞系统。不确定性和时滞是影响中立型系统性能的重要因素,因此对不确定中立型时滞系统的研究是系统控制问题研究的重要内容,也是难点内容。本文针对中立型时滞系统,在不确定性满足一定的假设条件下,研究其鲁棒稳定性。1.研究具有离散时滞与分布时滞的中立型系统的鲁棒稳定性问题。首先,通过构造适当的Lyapunov泛函,结合不等式分析技巧,给出了系统与分布时滞相关的鲁棒稳定性条件;然后,通过构造另外的Lyapunov泛函,引入含有自由矩阵的恒等式,再结合矩阵不等式,推出了系统与离散时滞和分布时滞相关的鲁棒稳定性条件。上述条件均能转化为线性矩阵不等式。最后,构造了相应的算例对所得结果的有效性进行验证。2.研究中立型时变时滞系统的指数稳定性问题。针对两种不同的初始状态空间,即连续的初始状态空间和连续可微的初始状态空间,运用Razuminkhin-Lyapunov技巧,获得了系统时滞无关的指数稳定性充分条件。更多还原

【Abstract】 During establishing models for practical control systems, there are discrepancies between the system model and the practical problems which can be described as uncertainties of systems resulting from inevitable measurement error, various interference and unmodelled dynamics, and so on. In addition, there always exist time delays in the system. Time delays not only exist in the state, but also may appear in the state change rate, that is so called neutral systems with time delays. Uncertainty and time delays are important factors which affect the performance of neutral systems. Therefore, the research on uncertain neutral systems with time delays is an important and difficult part in the research on the problems of system control. In this paper the robust stability of neutral systems with time delays is investigated, assumed that the uncertainties in the system satisfy some conditions.1. The problem of the robust stability for neutral systems with discrete and distribution time delays is investigated. Firstly, by constructing appropriate Lyapunov functional combined with the analysis technique of the inequality, the condition of distributed-delay-dependent robust stability of the system is present. Then by constructing appropriate Lyapunov functional and introducing zero equations with free-weighting matrices, together with using linear matrix inequalities, discrete-delay-dependent and distributed-delay-dependent robust stability condition of the system is deduced. Those conditions can be translated into linear matrix inequalities. Finally, a number of examples are presented to validate the effectiveness of the proposed results.2. The problem of exponential stability for neutral systems with time-varying delays is investigated. By employing the Razumikhin-Lyapunov technique, the sufficient conditions of delay-independent exponential stability are obtained for both different initial state space which are continuous initial state space and continuously differentiable initial state space.更多还原