【作者】 孙文安；

【导师】 赵军；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2006， 博士

【摘要】 本文研究线性切换系统鲁棒控制问题。主要研究鲁棒二次稳定性问题、鲁棒H_∞控制问题和鲁棒保成本控制等问题。主要内容归纳如下： 研究了具有凸锥型不确定性的线性切换系统的鲁棒二次稳定性问题。这种不确定性由若干已知常数矩阵所张成的凸锥来描述。利用凸组合技术，分别给出了连续和离散线性切换系统的鲁棒二次可稳定条件及切换律的设计方法。按照这些条件，只要判断张成凸锥的顶点矩阵的某个凸组合是否可稳即可。 利用完备性理论给出了具有多胞型摄动的线性切换系统的二次稳定的充分必要条件，利用单Lyapunov函数方法和多Lyapunov函数方法给出两个充分条件及切换律的两种设计方案。 构造区间矩阵，把线性切换系统转化为区间系统，利用线性矩阵不等式(LMI)给出了在任意切换策略下线性切换系统二次稳定的充分条件，这个条件可保证共同二次Lyapunov函数的存在性，但按通常的共同二次Lyapunov函数判定条件需要求解若干个LMIs，当子系统较多时计算量是相当大的，而这个条件只需找到一个LMI的解就可以判定该系统的二次稳定性，大大降低了计算工作量。 讨论了一类具有非线性摄动的线性切换系统在任意切换律下的二次鲁棒稳定性问题。首先利用Riccati不等式导出了具有时变摄动的在任意切换律下二次鲁棒稳定的充分条件，然后利用LMIs研究了具有非线性摄动项的线性切换系统在任意切换律下的二次鲁棒稳定的充分条件。 基于LMIs技术，研究了一类不确定线性切换系统在任意切换策略下的H_∞鲁棒控制问题。系统矩阵和输入矩阵都含有时变不确定性，利用矩阵Schur补引理构造LMIs，得到了在H_∞意义下的渐近稳定性的充分条件，同时也给出了在状态反馈下和输出反馈下的H_∞鲁棒控制问题可解的充分条件，并设计出控制器。 研究了一类不确定离散和连续系统的混杂状态反馈和输出反馈的二次稳定保成本H_∞控制问题。假设存在有限个备选的控制增益已知的控制器，利用共同更多还原

【Abstract】 This dissertation studies robust control problem for classes of switched linear systems, focusing on the problems of robust quadratic stability, robust H_∞ control and guaranteed cost control. The main results are summarized as follows.The problem for robust quadratic stability of switched linear systems with uncertainties of convex cone is discussed. The uncertainties form a convex cone spanned by a number of constant known matrixes. By using the convex combination method, quadratic stability conditions are derived for continuous switched linear systems and discrete switched linear systems, respectively. Only the matrixes of extreme points are involved in the conditions. The associated switching laws are also designed.By using the concept of completeness, a necessary and sufficient condition that guarantees quadratic stability is given for switched linear systems with polytopic perturbations. With single-Lyapunov function method and multiple-Lyapunov function method, sufficient conditions for quadratic stability are given with switching laws constructed.An interval matrix is introduced to transform a switched linear system into an interval system. A sufficient condition for quadratic stability of switched linear systems under arbitrary switching laws is presented in terms of linear matrix inequality. This condition implies the existence of a common quadratic Lyapunov function for all subsystems. While this condition is much simpler than usual conditions for the existence of a common quadratic Lyapunov function because only one linear matrix inequality needs to be solved while a number of linear matrix inequalities are involved in usual common quadratic Lyapunov function method. This is even more obvious when the number of subsystems is large.The quadratic robust stability problem for a class of switched linear systems and these systems with certain nonlinear perturbations under arbitrary switching laws is investigated. Sufficient conditions for quadratic robust stability are established by Riccati inequalities respectively for switched linear systems with time-variant perturbations and certain nonlinear perturbations under arbitrary switching laws.The problem of H_∞, robust control for uncertain switched linear systems under更多还原