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某些非线性系统可以通过全局线性化方法 ,转化为线性时变系统 ,因而可通过研究全局线性化后的线性时变系统来处理非线性系统的相关问题 .基于这一思路 ,利用线性微分包含的概念 ,对一类可化为多胞型线性微分包含的非线性系统 ,给出其基于观测器的 H∞输出反馈设计方法 ,得到的反馈控制律能使闭环系统内稳且具有 H∞干扰衰减 .文中对双边投影引理和 Finsler引理进行了扩展 ,从而可以处理基本矩阵不等式中块对角矩阵的消去问题 .利用这一结果 ,把基于观测器的 H∞ 输出反馈设计的一充分条件化为线性矩阵不等式 (L MI) ,进而利用已有的L MI工具箱对控制律进行求解 .从而避免了采用非线性系统设计的一般方法时必须面对的求解 Ham ilton- Jacobi不等式或等式方程的困难 .
Some nonlinear systems can be transformed into linear time-varying systems through the global linearization method, so we can deal with the related problems of nonlinear systems by studying the global linearized time-varying systems. Based on this idea, , An observer-based H∞ output feedback design method is presented for a class of nonlinear systems that can be considered as a polytopic linear differential inclusion. The resulting feedback control law enables the closed-loop system to be robust and has H∞ interference The paper extends the bilateral projection lemma and the Finsler lemma so that the elimination of the block diagonal matrix in the basic matrix inequality can be dealt with.Using this result, a sufficient condition for the observer-based H∞ output feedback design (LMI), and then use the existing LMI toolbox to solve the control law, so as to avoid solving the Hamilton-Jacobi-Inequality or Equations when using the general method of nonlinear system design The difficulty of the equation.