Stability analysis of set trajectories for families of impulsive equations.

*(English)*Zbl 1417.34117Authors’ abstract: “In this paper, for a family of impulsive equations, a heterogeneous matrix-valued Lyapunov-like function is considered, the comparison principle is formulated, and stability conditions for the set of stationary solutions are established. In addition, for a class of impulsive equations with uncertain parameters the monotone iterative technique for constructing a set of solutions is adapted.”

In Section 6 ‘Notes and comments’, the authors emphasize the contribution of the following references: [the first author, Russ. Acad. Sci., Dokl., Math. 50, No. 2, 1 (1994; Zbl 0864.34007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 338, No. 6, 728–730 (1994)], [M. Z. Djordjevic, Large Scale Syst. 5, 255–262 (1983; Zbl 0538.93048)], [J. Vasundhara Devi and A. S. Vatsala, Nonlinear Stud. 11, No. 4, 639–658 (2004; Zbl 1080.34004)] and [G. S. Ladde et al., Monotone iterative techniques for nonlinear differential equations. Boston-London: Pitman (Advanced Publishing Program); New York: John Wiley & Sons, Inc. (1985; Zbl 0658.35003)].

In Section 6 ‘Notes and comments’, the authors emphasize the contribution of the following references: [the first author, Russ. Acad. Sci., Dokl., Math. 50, No. 2, 1 (1994; Zbl 0864.34007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 338, No. 6, 728–730 (1994)], [M. Z. Djordjevic, Large Scale Syst. 5, 255–262 (1983; Zbl 0538.93048)], [J. Vasundhara Devi and A. S. Vatsala, Nonlinear Stud. 11, No. 4, 639–658 (2004; Zbl 1080.34004)] and [G. S. Ladde et al., Monotone iterative techniques for nonlinear differential equations. Boston-London: Pitman (Advanced Publishing Program); New York: John Wiley & Sons, Inc. (1985; Zbl 0658.35003)].

Reviewer: Yong-Kui Chang (Xi’an)

##### MSC:

34D20 | Stability of solutions to ordinary differential equations |

34A37 | Ordinary differential equations with impulses |

34A45 | Theoretical approximation of solutions to ordinary differential equations |

##### Keywords:

family of impulsive equations; stability; comparison principle; monotone iterative technique
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\textit{A. A. Martynyuk} and \textit{I. M. Stamova}, Appl. Anal. 98, No. 4, 828--842 (2019; Zbl 1417.34117)

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##### References:

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[12] | Djordjevic, MZ, Stability analysis of large scale systems whose subsystems may be unstable, Large Scale Syst, 5, 255-262, (1983) · Zbl 0538.93048 |

[13] | Vasundhara Devi, J.; Vatsala, AS, Monotone iterative technique for impulsive and set differential equations, Nonlinear Stud, 11, 639-658, (2004) · Zbl 1080.34004 |

[14] | Ladde, GS; Lakshmikantham, V.; Vatsala, AS, Monotone iterative techniques for nonlinear differential equations, (1985), Boston (MA): Pitman, Boston (MA) |

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