关键词: 广义非线性系统, 广义Lyapunov函数, 零解渐近稳定, H∞范数约束, 状态反馈

Abstract: The design of static state feedback H∞ controllers is discussed for a special class of nonlinear singular systems of which the state equation can be divided into linear part and nonlinear part. By means of the generalized Lyapunov function and Lyapunov equation, a sufficient condition that a nonlinear singular system is zero solution asymptotically stable is given. A sufficient condition is derived in terms of algebraic Riccati inequality which makes the nonlinear singular system zero solution asymptotically stable with a H∞ norm constraint. The existence condition of a state feedback H∞ controller is presented, guaranteeing that the resulting closed-loop system has above performance. The design method of such a controller is provided in terms of the solution to Lyapunov equation. An example is given to prove the validity of the results.