Abstract
Under Neumann or Dirichlet boundary conditions, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs) is considered. Thanks to some methods different from those of previous literature, the difficulties brought by fuzzy stochastic mathematical model and impulsive model have been overcome. By way of the Lyapunov-Krasovskii functional, Itô formula, Dynkin formula and a differential inequality, new LMI-based global stochastic exponential stability criteria for the above-mentioned PDEs are established. Some applications of the obtained results improve some existing results on neural networks. And some numerical examples are presented to illustrate the effectiveness of the proposed method due to the significant improvement in the allowable upper bounds of time delays.MSC:34D20, 34D23, 34B45, 34B37, 34K20.
Highlights
1 Introduction In this paper, we are concerned with the following delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs):
Author details 1Institution of Mathematics, Yibin University, Yibin, Sichuan 644007, P.R. China
Summary
We are concerned with the following delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs):. If the following three conditions hold: (E ) there exist a sequence of positive scalars α and positive definite diagonal matrices P such that the following LMI conditions hold:. (E ) there exists a constant δ > such that infk∈Z(tk – tk– ) > δτ , δ τ > ln(ρeλτ ) and λ λmax(H|N T |P|N λmin P. unique solution of the equation λ = a – beλτ , the null solution of impulsive stochastic system (n|d|A Gλmax λmin P (F ) there exists a constant δ > such that infk∈Z(tk – tk– ) > δτ , δ τ > ln(ρeλτ ) and λ supj∈Z
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