Large-scale stochastic hereditary systems under Markovian structural perturbations. Part III. Qualitative analysis

[摘要] In this final part of the work, the convergence and stabilityanalysis of large-scale stochastic hereditary systems under randomstructural perturbations is investigated. This is achievedthrough the development and the utilization of comparison theoremsin the context of vector Lyapunov-like functions anddecomposition-aggregation method. The byproduct of theinvestigation suggests that the qualitative properties ofdecoupled stochastic hereditary subsystems under random structuralperturbations are preserved, as long as the self-inhibitoryeffects of subsystems are larger than cross-interaction effects ofthe subsystems. Again, it is shown that these properties areaffected by hereditary and random structural perturbationseffects. It is further shown that the mathematical conditions arealgebraically simple, and are robust to the parametric changes.Moreover, the work generates a concept of block quasimonotonenondecreasing property that is useful for the investigation ofhierarchic systems. These results are further extended to theintegrodifferential equations of Fredholm type.

[学科分类] 应用数学