离散Lipschitz非线性系统状态和未知输入估计
State and unknown input estimations for discrete-time Lipschitz nonlinear systems

针对含有未知输入和可测噪声的离散Lipschitz非线性系统, 研究了状态估计、未知输入以及可测噪声同时 估计的问题. 首先, 对含有未知输入的系统, 设计了比例积分观测器, 达到同时估计系统状态和未知输入之目的. 分 析了残差系统的观测性和稳定性, 利用H1实现该观测器对时变未知输入的有效估计; 其次, 将观测器增益矩阵的 求解转化为求解线性矩阵不等式的形式; 进一步地, 基于系统状态扩展方法, 将所提方法推广至同时含有未知输入 和可测噪声的系统; 最后, 通过两个仿真算例说明了所提方法的正确性和有效性.
The discrete-time Lipschitz nonlinear systems that subjected to unknown inputs and measurement noises, state, unknown input and measurement estimations simultaneously are investigated in this paper. Firstly, a proportional integral observer is designed for estimating system states and unknown inputs on system with unknown inputs. Both of the observability and the stability of the residual system are analyzed. The effective estimation of time-varying unknown inputs is finished by using H1. And then, the problem of solving observer gain matrix is transformed into calculating a linear matrix inequality. Further more, based on the system expansion, the proposed method is extended to the system that with both unknown inputs and measurement noises. Finally, the correctness and the effectiveness of presented methods are illustrated via two simulation examples.