Stability and Boundedness of Solutions to Some Non-autonomous Multidimensional Nonlinear Systems

TL;DR

This paper introduces an improved method for assessing the stability and boundedness of solutions to complex nonlinear systems with time-varying coefficients, enabling more accurate and computationally feasible analysis.

Contribution

It develops a novel technique that extends the application domain and reduces computational complexity of previous stability assessment methods for nonlinear systems.

Findings

More general boundedness/stability criteria established

Enhanced estimation of stability regions in nonlinear systems

Application to systems previously intractable with earlier methods

Abstract

Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the known techniques provide computationally intensive and conservative stability criteria in this field and frequently fail to estimate the regions of boundedness/stability of solutions to the corresponding systems. Recently, we outlined a new approach to this problem which is based on the analysis of solutions to a scalar auxiliary equation bounded from the above time histories of the norms of solutions to the original system. This paper develops a novel technique casting the auxiliary equation in a modified form which extends the application domain and reduces the computational hamper of our prior approach. Consequently, we developed more general boundedness/stability criteria and estimated trapping/stability regions for some multidimensional nonlinear systems with nonperiodic time-dependent coefficients that are common in various application domains. This let us to assess in target simulations the extent of boundedness/stability of some multidimensional, nonlinear and time-varying systems which were intractable with our prior technique.