Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks. (English) Zbl 1490.34060
Summary: This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results.
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 34A37 | Ordinary differential equations with impulses |
| 34H05 | Control problems involving ordinary differential equations |
| 05C20 | Directed graphs (digraphs), tournaments |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
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