一类混合时滞系统的观测器设计

对于一类具有状态和有限自动机输出时滞的离散混合系统，给出了混合观测器的设计方法。观测器由一个位置观测器和一个离散状态观测器组成。前者应用自动机观测器来确定混合系统的当前位置，后者应用龙伯格观测器对系统离散状态的演化进行估计。对于每一个独立的观测器，系统的信息往往不完全，为了在这种情况下仍能应用混合观测器对系统进行观测，在两类独立观测器的基础上给出了一个新的信号产生器，将两类观测器有机结合起来。同时给出了信号产生器中决策函数的充分条件，进一步得到了整个混合观测器指数收敛的充分条件。保证该混合观测器能在有限步内判断出系统的当前位置，同时指数收敛于真实离散时间状态。最后，给出了仿真例子说明设计方法的可行性和有效性。

Design of observers for a class of hybrid systems with time delay

An observers design methodology was proposed for a kind of discrete hybrid systems with state delay and location identification delay. The hybrid observer was made up of a location observer and a discrete time state observer. The location observer defined the current location of the hybrid system by Finite State Machine (FSM), while the discrete time state observer estimated the evolution of the discrete time state of the hybrid system by Luenberger observers. However, the information of system for each observer was usually not perfect. In order to solve this problem, a new signal generator was developed based on the proposed hybrid observer to combine two kinds of observers. An abundant condition enabling the Decision Function in the signal generator was given, and then the abundant condition to guarantee the exponential convergence of the hybrid observer was also provided. The hybrid observer identified the current location of the plant in a finite number of steps and converged exponentially to the discrete time state.. Finally, a simulation example was provided to illustrate the feasibility and the effectiveness of the proposed method.