Abstract
Considering the limitation of machine and technology, we study the stability for nonlinear impulsive control system with some uncertainty factors, such as the bounded gain error and the parameter uncertainty. A new sufficient condition for this system is established based on the generalized Cauchy–Schwarz inequality in this paper. Compared with some existing results, the proposed method is more practically applicable. The effectiveness of the proposed method is shown by a numerical example.
Highlights
Impulse control is based on impulsive differential equation and has many applications [1,2,3,4,5,6], such as digital communication system, artificial intelligence, and financial sector
In comparison with other methods, impulse control is more efficient in dealing with the stability of complex systems. e stability is an important property of the impulsive control system
To make the nonlinear impulse control system more reasonable, parameter uncertainty and bounded gain error are introduced into the corresponding impulsive differential equations [22,23,24,25]
Summary
Impulse control is based on impulsive differential equation and has many applications [1,2,3,4,5,6], such as digital communication system, artificial intelligence, and financial sector. To make the nonlinear impulse control system more reasonable, parameter uncertainty and bounded gain error are introduced into the corresponding impulsive differential equations [22,23,24,25]. Zou et al study impulsive systems with bounded gain error and form a sufficient criterion for the stability [27]. Cauchy–Schwarz inequality is an important tool to study nonlinear systems [28,29,30,31]. Peng et al generalize the Cauchy–Schwarz inequality, which is used to deduce asymptotic stability for a class of nonlinear control systems [30]. Based on the generalized Cauchy–Schwarz inequality, we consider a class of nonlinear impulsive control systems with the parameter uncertainty, which can be written as follows:.
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