【作者】 焦艳会；

【导师】 陈东彦；

【作者基本信息】 哈尔滨理工大学 ， 应用数学， 2005， 硕士

【摘要】 自七十年代以来,由于系统空间上的大型化和结构上的复杂化等因素,在工程技术、社会经济和生态生物等领域中提出了规模庞大,结构复杂的大系统模型。因此对含有不确定项的时滞关联大系统的鲁棒稳定性分析问题的深入研究不仅能完善控制系统的理论基础,而且将极大地推动控制理论在实际中的应用。　本文主要探讨了具有常时滞和变时滞的不确定关联大系统的鲁棒稳定性条件。将关于时滞大系统稳定性分析的某些成果推广到含有不确定性的情况之中;将M 矩阵和线性矩阵不等式(LMI)方法应用到不确定时滞关联大系统的鲁棒稳定性研究中。具体包括以下三部分内容: 1.考虑常时滞的不确定关联大系统,针对具有强结构不确定性、非结构不确定性和矩阵多胞型结构不确定性情形,利用Lyapunov 函数,结合拉什密辛定理,和代数不等式技巧,分别给出了相应系统的时滞无关的鲁棒稳定性判别条件。并给出部分算例验证了所得结果。　2.考虑常时滞的不确定关联大系统,针对具有强结构不确定性和非结构不确定性不确定性情形,通过构造适当的Lyapunov 函数,并利用M 矩阵的性质,给出了系统时滞无关的鲁棒稳定充分条件。3.考虑变时滞的不确定关联大系统,针对具有强结构不确定性、矩阵多胞型结构不确定性和范数有界不确定性的情形,利用Lyapunov 函数和LMI方法,得出了系统鲁棒稳定的时滞无关的判别条件。更多还原

【Abstract】 Since 1970s, large-scale system models have been applied to the realm of engineering technology, economy and ecology since the extension of system space and the complication of system structure. A more deep investigation on the robust stability for linear uncertain interconnected large-scale systems with time-delays not only perfects the foundation of control theory, but also promotes the implementation of such theory in practice. This paper mainly discusses the robust stability for linear uncertain interconnected large-scale systems with constant time-delays and varying time-delays. Some results of large-scale systems with time-delays are extended to interconnected large-scale systems with uncertainty, and M matrix and linear matrix inequality method are applied to the investigation of the robust stability for linear uncertain interconnected large-scale systems. Main results of this paper include the following three parts: 1. The problem of robust stability is studied for the uncertain interconnected large-scale systems with constant time-delays. Under high structured uncertainty, unstructured uncertainty and matrix polytope structured uncertainty assumptions, the sufficient conditions of robust stability are derived by using Lyapunov function and Razumikhin theorem. Some examples are given to illustrate them. 2. The robust stability for the uncertain interconnected large-scale systems with constant time-delays is studied. We give the sufficient conditions of robust stability for high structured uncertainty and unstructured uncertainty assumptions based on Lyapunov functional method and the properties of M matrix. 3. The problem of robust stability is studied for the uncertain interconnected large-scale systems with varying time-delays. The sufficient conditions of robust stability are derived under high structured uncertainty, matrix polytope structured uncertainty and norm bounded uncertainty by using Lyapunov function and LMI method. All the principles are time-delay independent.更多还原