Series expansions for analytic systems linear in control

This paper presents a series expansion for the evolution of a class of nonlinear systems characterized by constant input vector fields. We present a series expansion that can be computed via explicit recursive expressions, and we derive sufficient conditions for uniform convergence over the finite and infinite time horizon. Furthermore, we present a simplified series and convergence analysis for the setting of second order polynomial vector fields. The treatment only relies on elementary notions on analytic functions, number theory, and operator norms. Key words: nonlinear systems, perturbation theory, Volterra series

• Type: Journal
• Year: 2002
• Where: AUTOMATICA
• Authors: Francesco Bullo
• Keywords: AUTOMATICA 2002, Nonlinear Systems, Series Expansion, Vector Fields