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

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 are 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.

Optimal Dichotomy of Temporal Scales and Boundedness/ Stability of Time – Varying Multidimensional Nonlinear Systems

“…This paper contributes a novel approach to the assessment of the behavior of the norms of solutions to VNDS, which rests on the development of the scalar auxiliary counterparts to such systems. This effort extends our studies that were concerned with the dynamics of similar systems in finite dimensions [29]- [32]. We show that the solutions to such auxiliary delay equations bound from the above evolution of the norms of solutions to the original VNDS with matched history functions.…”