摘要在现实生活中存在这一类特殊的系统，它们的状态变量始终为正（或至少非负），具有这种特点的系统称之为正系统。正系统在诸多领域有重要应用，如生物、物理、化学、通讯、经济等领域。在这些领域内的某些情形下，如果状态变量为负值，研究就失去了意义。由于一般分析动力学性质的方法不能有效利用正系统的特性，忽略了状态为负的特殊性。另一方面，当系统受到外部干扰时，如何设计保性能控制器使得系统性能上界减小，保守性降低，以改善系统的瞬态性与鲁棒性是本次论文有待解决的问题。65319

     本论文分别对线性连续系统、线性离散系统（并考虑了他们的不确定性），结合一个二次型性能指标，讨论了当执行机构发生故障情况下的可靠保性能状态反馈控制律的设计问题。另外，系统也会因为其他一些外部因素，例如系统使用时间过长，加之使用之后不注意保养导致设备的性能变差，由此会造成实际的结果与理想中的结果产生偏差。通过运用线性矩阵不等式（LMI）的研究方法，研究了线性系统的保性能控制律存在的条件，并推出该条件等价的LMI的可解性问题，进而将所有可靠保性能控制器用一个参数化的形式表示出来。对于线性连续系统与线性离散系统（包括不确定系统），通过研究系统的保性能控制，来说明对系统进行保性能控制设计的重要性和必要性。

毕业论文关键词：线性矩阵不等式（LMI）、线性连续系统、线性离散系统、不确定性、保性能、正系统。

毕业设计说明书（论文）外文摘要

Title  The  Optimal Guaranteed Cost Control  of Positive Linear Systems   

   ABSTRACT  

    In real life there is a special class of systems, their state variable is always positive (or at least non-negative), a system with this feature is called positive systems. Positive systems have important applications in many fields, such as biology, physics, chemistry, communications, economics and other fields. In some cases in these areas, if the state variable is negative, the study would be meaningless. Due to the general nature of the kinetic analysis methods cannot effectively use positive characteristics of the system, we ignore the state for the negative specificity. On the other hand, when the system is subject to external interference, how to design a security system, which can make the upper bound of the performance decreases and lower the conservatism, and how to improve the transient and robustness of the system are the major problems to be solved in this thesis.

The paper focuses on linear continuous systems, linear discrete systems (with or without uncertainties), combined with a quadratic performance index, discusses the reliable guaranteed cost state feedback control law design problem when the actuator is out of control. In addition, certain external factors, such as the system was used for too long, or people paid no attention to nurturing result, may lead to the system falling into a poor condition and the actual results different from those derived in an ideal situation. Through the use of LMI method to study the sufficient condition of guaranteed cost controller design for the linear system, the launch of the LMI condition is equivalent to the solvability of the problem, and then all the reliable guaranteed cost controllers can be characterized by a parametric representation of it. For linear continuous systems and linear discrete systems (uncertainties involved in systems), the studying of the performance of the system security shows that the system guaranteed cost control design is important and necessary from a practical standpoint.

Keywords:  Guaranteed cost control, Linear continuous systems, Linear discrete systems, Linear matrix inequality (LMI), Positive systems, Uncertainty.