一类不确定非线性广义时滞系统的H_∞控制

H_∞ Control for a Class of Uncertain Nonlinear Singular Systems with Time-delay

针对一类具有非线性控制输入的参数不确定广义时滞系统,研究了该类广义系统的鲁棒H∞控制问题。利用Lyapunov泛函方法和线性矩阵不等式工具,无需对广义系统进行转化,得到了闭环系统鲁棒渐近稳定且具有H∞范数界的充分条件;将其转化为不带参数不确定矩阵的线性矩阵不等式,基于相应的线性矩阵不等式可行解,给出了该类广义系统的H∞控制律的构造方法。数值例子表明了该方法的有效性和可行性。

The robust H∞ control problem for a class of uncertain nonlinear control input singular systems with time-delay is discussed. By means of Lyapunov function and linear matrix inequalities （LMIs）, a sufficient condition is presented to guarantee that the closedloop system is robust asymptotic stability, and satisfies a prescribed H∞ norm-bounded constraint. Then the sufficient condition is transformed to an LMI without the uncertainty parameter matrix. Based on solutions of LMIs, the H, state feedback control law of singular system is presented. A numerial simulation example shows the effectiveness and feasibility of proposed method.