Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-02-28 DOI:10.1007/s00332-024-10013-x

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Abstract

Assessment of the stability/boundedness of solutions to nonlinear systems with variable coefficients brings long-standing and challenging problems which emerge in various application domains. These problems naturally evolved into more arduous and largely open problems concerned with the estimation of the corresponding stability/boundedness regions. This paper develops a novel approach furnishing computationally tractable boundedness/stability criteria which underscores a methodology providing recursive estimation of the boundaries of the trapping/stability regions for a broad class of multidimensional and nonlinear systems with variable nonperiodic coefficients. Furthermore, our approach naturally conveys the bilateral bounds for the norms of solutions to the corresponding systems via the application of successive approximations which are introduced in this paper. The developed techniques are validated in inclusive simulations which endorse their applications to systems with large and complex nonlinear components and bounded in-norm time-varying disturbances.

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某些时变系数多维非线性系统的陷阱/稳定区域和双边解边界的有效估计

摘要对具有可变系数的非线性系统的解的稳定性/有界性进行评估，是一个长期存在且具有挑战性的问题，它出现在各种应用领域。这些问题自然而然地演变成了更为艰巨的问题，而且在很大程度上与估计相应的稳定性/有界性区域有关。本文开发了一种新方法，提供了可计算的有界性/稳定性标准，强调了一种方法论，为一大类具有可变非周期性系数的多维非线性系统提供陷阱/稳定性区域边界的递归估计。此外，我们的方法通过应用本文介绍的连续近似法，自然地传达了相应系统解规范的双边边界。本文所开发的技术已在大量模拟中得到验证，这些模拟支持其在具有大型复杂非线性成分和有界时变扰动的系统中的应用。

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