Improved delay-dependent stability of superlinear hybrid stochastic systems with general time-varying delays

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Abstract

In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.
Original languageEnglish
Article number101413
Number of pages19
JournalNonlinear Analysis: Hybrid Systems
Volume50
Early online date22 Aug 2023
DOIs
Publication statusPublished - 30 Nov 2023

Keywords

  • delay-dependent stability
  • super linearity
  • hybrid stochastic delay systems
  • Lyapunov functional

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