一类不确定非线性系统的观测器设计

系统状态观测器在故障检测与状态反馈中起着重要作用，特剐是非线性系统状态观测器的构造已成为目前控制理论界一个重要研究课题。本文针对一类含有建模误差的非线性系统，提出了一种非线性状态观测器的结构形式，然后利用非线性变换，将含有建模误差的非线性系统变换为仅依赖原系统的输入、输出的规范形式，从而利用可测数据进行构造观测器。在此基础上，利用Lyapunov稳定性理论以及微分同胚的性质，分析了非线性动态误差方程的稳定性。理论证明，在建模误差为零时，估计状态收敛到其真实状态；在建模误差不为零时，估计状态与实际状态之差一致最终有界。最后进行了详细的仿真研究，结果表明了该方法的有效性。

State Observer Design for a Class of Nonlinear Systems with Modelling Uncertainty

The state observer plays an important role in fault detection and states feedback control. Recently, much attention has been focused on the struction of the state observer in nonlinear systems. This paper presents a state observer for a class of nonlinear systems with modelling uncertainty. Firstly, the nonlinear system is analyzed and diffeomorphically transformed into a canonical system, thus using measurable output to design the state observer. Based on Lyapunov stability theory and properties of diffeomorphism, the stability of dynamical error equation is proved and two conclusions are given: when modelling uncertainty is not existed, the estimated states are convegence states of the system; when modelling uncertainty is bounded, the error between the estimated states and the system states is ultimately and uniformely bounded. Simulation examples illustrate the effectiveness of the approach.