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**Second method of Lyapunov and comparison principle for systems with impulse effect.**
*(English)*
Zbl 0729.93052

Summary: Questions of stability and boundedness of the solutions of systems with impulse effect at fixed moments with respect to a manifold are considered. The investigations are carried out by means of piecewise continuous vector-valued functions which are analogues of Lyapunov’s functions. By means of a vector comparison equation and differential inequalities for piecewise continuous functions, we obtain theorems on stability and boundedness of the solutions of systems with impulses with respect to a manifold.

### MSC:

93C57 | Sampled-data control/observation systems |

34A40 | Differential inequalities involving functions of a single real variable |

34C11 | Growth and boundedness of solutions to ordinary differential equations |

34D20 | Stability of solutions to ordinary differential equations |

### Keywords:

systems with impulse effect
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\textit{G. K. Kulev} and \textit{D. D. Bainov}, J. Comput. Appl. Math. 23, No. 3, 305--321 (1988; Zbl 0729.93052)

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### References:

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