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Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms. (English) Zbl 1411.60114
Summary: The robust global exponential estimating problem is investigated for Markovian jumping reaction-diffusion delayed neural networks with polytopic uncertainties under Dirichlet boundary conditions. The information on transition rates of the Markov process is assumed to be partially known. By introducing a new inequality, some diffusion-dependent exponential stability criteria are derived in terms of relaxed linear matrix inequalities. Those criteria depend on decay rate, which may be freely selected in a range according to practical situations, rather than required to satisfy a transcendental equation. Estimates of the decay rate and the decay coefficient are presented by solving these established linear matrix inequalities. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.

MSC:
60J28 Applications of continuous-time Markov processes on discrete state spaces
35K51 Initial-boundary value problems for second-order parabolic systems
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