一类Lipschitz非线性时滞离散广义系统降维观测器的设计

Design of reduced-order observer for a class of Lipschitz nonlinear time-delay discrete generalized system

针对时滞离散广义系统降维观测器的设计问题,提出一类Lipschitz非线性时滞离散广义系统降维观测器的设计方法。首先,基于时滞离散广义系统的可观性对系统进行变换,将系统变换为易于求取降维观测器的形式;其次,基于非线性系统观测器设计的Lyapunov稳定性理论,通过讨论时滞系统中的Lipschitz非线性项,分两种情况设计出了时滞系统的两个降维观测器;最后,为使得时滞系统与降维观测器的误差系统渐近稳定,利用线性矩阵不等式(LMI)的方法分别给出了两个降维观测器存在的充分条件,并通过数值算例验证了该类降维观测器设计方法的有效性。

The design of reduced order observers for discrete time singular systems with time-delay are studied,a design method of observer for a class of nonlinear systems is presented.Firstly,the system is transformed based on the observability of time-delay discrete generalized system,and the system is transformed into the form of reduced dimensional observer;Secondly,two reduced-order observer for time-delay system are designed by discussing the nonlinear term of Lipschitz in time-delay system based on the Lyapunov stability theory of nonlinear system observer design;Finally,in order to make the error system of the delay system and the reduced dimensional observer asymptotically stable,the sufficient conditions for the existence of two reduced dimensional observers are given by using the linear matrix inequality (LMI) method,and the numerical example is given to verify the validity of the design method of this kind of observer.