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EXISTENCE RESULTS FOR A CLASS OF HYBRID SYSTEMS WITH INFINITE DELAY

In this paper, the existence, uniqueness, and continuation of solutions to switched systems with infinite delay and impulses is investigated. Both time-dependent and state-dependent switching are considered. The main results on existence and unique- ness are proved by adjusting classical techniques to account for impulses, infinite delay, and switches. Extended and global existence results are given for different types of switch- ing rules. The results found are also applicable to impulsive switched systems with finite delay. An epidemic model is presented to illustrate the results.