一类更普遍Lipschitz非线性系统状态观测器设计

摘要

本文采用求解状态方程的方法,结合(Gronwall-Bellman不等式讨论了一类非线性系统状态观测器的设计问题.此类系统的非线性项是全局Lipschitz的.针对于原系统、原系统的约当规范形分三种情形给出了观测器渐近收敛的充分条件.结论表明:稳定观测器的存在直接与误差系统的稳定性矩阵测度及增益矩阵的范数有关.借助于相应的优化算法给出了增益矩阵的选取.文末通过仿真验证了结论的有效性.%In this paper state observer design for a class of nonlinear systems is discussed by solving state equations and utilizing the Gronwall-Bellman inequality. The nonLinear items of the class of systems are globally Lipschitz. The sufficient conditions ensuring asymptotic stability of the observer are presented in three cases for the original systems and the transformed systems in Jordan canonical form. The conclusions show that the existence of stable observers for the class of systems is related straightly to the matrix measures of the stability matrix of the error dynamics and the norm of gain matrix. The gain matrix is chosen with the aid of an optimization algorithm. Finally the conclusions are validated by simulation.