关键词: Lipschitz系统, 非线性系统, 观测器设计, Riccati方程, 奇异值

Abstract: The observer design is investigated for a class of more general Lipschitz nonlinear systems. The problem of asymptotically convergent observer design is changed into solving the corresponding gain matrix. The sufficient conditions satisfied by the gain matrix are given, and the method of solving gain matrix is also presented. First, under certain detectability that the system satisfies, the sufficient conditions are presented for the asymptotic convergence of the observer error by using the singular value theory. The method of solving gain matrix is presented based on the Riccati equation. Second, when the system does not satisfy such detectability but satisfy other conditions, there is a gain matrix ensuring the asymptotic convergence of the observer error, and the sufficient conditions and the method of solving gain matrix are obtained similarly. Two simulation examples are given to demonstrate correctness of the theoretical results.

Key words: nonlinear system, observer design, Riccati equation, singular value , Lipschitz system