Abstract: To study a class of linear time invariant sampling control system with periodic sample， the following steps were carried out. Firstly， the definition of system norm was given， and then the system was dispersed simultaneously by norm invariant transformation and step invariant transformation based on the definition of system norm to get the discretion model of the system. Secondly， fault detection problems of H_/H∞， H2/H∞ and H∞/H∞ were considered， and the form of the optimal filter was provided. At the same time， based on the design idea and method of the optimal filter for discrete system， the design method and form of the fault estimation observer were given out， and the essential condition of the error equation asymptotic stability was gotten by structuring Lyapunov function. What’s more， the fault estimation adaptive weighting matrix Γ and parameter θ were solved by Matlab LMI toolbox as well. At last， a numerical example was given to illustrate the effectiveness of the proposed method.

Key words: norm invariant, step invariant, sampling system, fault detection, fault estimation