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

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.