Abstract: Based on Lyapunov functional method,the reachable set boundary estimation problem for a class of singular semi-Markovi jump systems with time-varying delays is studied.Firstly,the boundary of the fast and slow subsystem is obtained by the piecewise analysis method and integral inequality technique.Then,the upper and lower boundary of semi-Markov transfer rate is used to deal with the problem of abnormal transfer rate.Finally,the sufficient condition of the existence of the reachable set boundary of the system is given in the form of linear matrix inequality.

Key words: time-varying delays, generalized semi-Markov jump systems, reachable set, linear matrix inequality