R. P. Agarwal, S. Hristova, D. O'Regan, P. Kopanov

p-Moment Exponential Stability of Differential Equations with Random Impulses and the Erlang Distribution

The investigation of differential equations with random impulses combines ideas in the qualitative theory of differential equations and probability theory. The p-moment exponential stability of the solutions is defined and studied when the waiting time between two consecutive impulses is Erlang distributed. The study is based on the application of Lyapunov functions. Some examples are given to illustrate the results.

Mathematics Subject Classification: 34F05, 60G17, 34A37, 34D20, 93E15

Key words and phrases: Impulsive differential equations, random moments of impulses, Erlang distribution, $p$-moment exponential stability