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Wang, Lei; Li, Xiaodi

\(\mu \)-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. (English) Zbl 1315.34079

Math. Methods Appl. Sci. 36, No. 11, 1140-1446 (2013).
The authors discuss the problem of \(\mu\)-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. Some \(\mu\)-stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using the Lyapunov-Krasovskii functional method. These criteria are expressed in the form of linear matrix inequalities which are easily checked. Moreover, two numerical examples are provided to demonstrate the effectiveness of the obtained results. Both the theoretical and numerical results seem interesting.
Reviewer: Binxiang Dai (Changsha)

Cited in 9 Documents

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses

Keywords:

\(\mu \)-stability; unbounded time-varying delays; impulsive differential systems; linear matrix inequality (LMI); nonlinear perturbations
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References:

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