Discussions on Existence of Observers and Reduced-order Observer Design for Discrete-time Switched Systems
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摘要: 对具有未知输入的离散切换系统讨论了未知输入观测器（Unknown input observer，UIO）设计方法.首先，对一般离散系统的未知输入观测器匹配条件的Lyapunov-type表示，进行了等价性论证；然后，基于不具有未知输入的离散切换系统的稳定性理论，对具有未知输入的离散切换系统提出了一种切换降维观测器设计方法.通过矩阵分块确定出的观测器增益矩阵，使得降维观测器能直接消去未知输入的影响；然后，在此基础上提出了一种未知输入代数重构方法；最后，通过仿真验证了方法的有效性和正确性.Abstract: The paper discusses the unknown input observer (UIO) design issue for discrete-time switched systems with unknown inputs. First, a Lyapunov-type equivalent representation of observer matching condition for a general discrete-time system is given and proved. Then, based on the stability theory of discrete-time switched system without unknown inputs, a reduced-order observer is developed for a discrete-time switched system with unknown inputs. The reduced-order observer can eliminate the influences of the unknown inputs directly because of the special selection of the observer gain matrix determined by matrix block computation. Meanwhile, an algebraic unknown input reconstruction method is proposed. Finally, a simulation example is given to verify the correctness and effectiveness of the proposed methods.
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