Successive Estimations of Bilateral Bounds and Trapping/Stability Regions of Solution to Some Nonlinear Non-autonomous Systems

TL;DR

This paper introduces a new method for accurately estimating stability, bounds, and trapping regions in nonlinear non-autonomous systems, improving over conservative existing techniques through successive approximation and error estimation.

Contribution

The paper presents a novel successive approximation methodology for estimating solution bounds and stability regions in nonlinear non-autonomous systems, with error bounds and improved criteria.

Findings

Provides more accurate bounds for solutions

Develops enhanced stability criteria

Validates results with simulations

Abstract

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are unable to effectively gage these characteristics in time-varying nonlinear systems. This paper develops a novel methodology providing successive approximations to solutions that are stemmed from the trapping and stability regions of these systems and estimate the errors of such approximations. In turn, this leads to successive approximations of both the bilateral bounds of solutions and the boundaries of trapping and stability regions of the underlying systems. Along these lines we formulate enhanced stability and boundedness criteria and contrast our inferences with inclusive simulations.