Abstract. 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 uniqueness 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 switching rules. The results found are also applicable to impulsive switched systems with finite delay. An epidemic model is presented to illustrate the results

Peter Stechlinski

Xinzhi Liu

CiteSeerX

Dynamics of Continuous, Discrete and Impulsive Systems
Series B: Applications & Algorithms 20 (2013) 591-623
Copyright c⃝2013 Watam Press
EXISTENCE RESULTS FOR A CLASS OF HYBRID
SYSTEMS WITH INFINITE DELAY
Xinzhi Liu and Peter Stechlinski
Department of Applied Mathematics
University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Abstract. 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.
Keywords. Existence; Uniqueness; Extended existence; Hybrid systems; Infinite delay.
Dynam. Cont. Dis. Ser. B, vol. 20, no. 6, pp. 591-623, 2013.
620 X.Z. Liu and P.G. Stechlinski
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Received September 2013; revised December 2013
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EXISTENCE RESULTS FOR A CLASS OF HYBRID SYSTEMS WITH INFINITE DELAY

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EXISTENCE RESULTS FOR A CLASS OF HYBRID SYSTEMS WITH INFINITE DELAY

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