Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

Abstract

In this paper we have established the sufficient conditions for asymptotic convergence of all solutions of nonlinear dynamical system (with potentially unknown and unbounded external disturbances) to zero with time t → ∞ . We showed here that the symmetric part of linear part of nonlinear nominal system, or, to be more precise, its time-dependent eigenvalues, play important role in assessment of the robustness of systems.

Keywords

• nonlinear system
• perturbation
• robustness
• variation of constants formula
• symmetric part of linear operator