基于跳变的广义时变系统的时域控制

发布时间：2018-03-16 15:23

  本文选题：广义时变系统　切入点：矩阵微分不等式　出处：《沈阳工业大学》2015年硕士论文　论文类型：学位论文

【摘要】：现代科技、社会科学各个领域的实际问题中往往会存在瞬时突变现象，这种现象不能用单纯的微分或差分方程来表示，而用基于跳变的微分方程描述更加合适。基于跳变的微分方程能够充分的考虑到瞬间突发现象对系统状态的影响，并且更深刻更精确的反映事物变化的规律。因此基于跳变的微分系统在工程实践中具有一定的应用价值。 本文研究了基于跳变的广义时变系统的时域控制问题。首先，研究了基于跳变的广义时变系统的输入输出时域稳定问题。基于矩阵微分不等式，对应于L2干扰输入给出了一个上述系统输入输出时域稳定的充分条件，并对应L干扰输入给出了一个上述系统输入输出时域稳定的充分条件。这样的条件要求矩阵微分不等式解的存在性。接下来根据给出的充分条件设计了控制器，使得闭环系统输入输出时域稳定。本文的结果对于一般情况下的广义时变系统是同样适用的。对于广义条件的非严格矩阵不等式给出了一种化简的方法将其转化为严格的矩阵不等式，对于时变的矩阵不等式给出了一种分段线性化的算法使得可以应用Matlab LMIs工具箱对其求解。最后，我们给出了两个算例来验证结果的有效性。 接下来，研究了带有时变不确定性的基于跳变的广义时变系统的时域H∞控制问题，给出了时域H∞控制的概念。首先给出了上述系统时域有界的充分条件，，然后将结论推广到时域H∞的情形并给出了一个充分条件。基于给出的充分条件设计了控制器使得闭环系统时域有界且满足L2增益。所有的条件都是以矩阵不等式和微分矩阵不等式的形式给出的，对于广义条件的非严格矩阵不等式给出了一种化简的方法将其转化为严格的矩阵不等式。对于时变的矩阵不等式给出了一种分段线性化的算法使得可以应用Matlab LMIs工具箱对其求解。最后给出了一个数值算例验证了结论的有效性。
[Abstract]:In modern science and technology, social science and social science, there is often a transient abrupt change in practical problems, which can not be expressed by a simple differential or difference equation. It is more suitable to describe the differential equation based on jump. The differential equation based on jump can fully take into account the effect of the instantaneous burst phenomenon on the system state. Therefore, the differential system based on jump has certain application value in engineering practice. In this paper, the time-domain control problem of generalized time-varying systems based on jump is studied. Firstly, the input and output time-domain stability of generalized time-varying systems based on jump is studied. Corresponding to the L2 interference input, a sufficient condition for the time-domain stability of the input and output of the system mentioned above is given. A sufficient condition for the time-domain stability of the input and output of the system mentioned above is given, which requires the existence of the solution of the matrix differential inequality. Then, the controller is designed according to the sufficient conditions given. The results obtained in this paper are also applicable to generalized time-varying systems under general conditions. A simplified method is given for the non-strict matrix inequalities with generalized conditions. For strict matrix inequalities, A piecewise linearization algorithm is presented for time-varying matrix inequalities, which can be solved by using the Matlab LMIs toolbox. Finally, two examples are given to verify the validity of the results. Then, the time-domain H _ 鈭

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