Estimation of Regions of Attraction for Time-Varying Uncertain Nonlinear Systems Modeled by a Particular Class of Linear Differential Inclusion

[摘要] This paper proposes the use of a particular class of linear differential inclusion (LDI) for the estimation of regions of attraction of asymptotically stable equilibrium points of nonlinear dynamical systems with time-varying parametric uncertainties bounded by a polytope. In this paper, we provide a systematic procedure based on the mean value theorem in conjunction to a linear matrix inequality based approximation technique to obtain the description of the uncertain nonlinear system via the proposed LDI form, which can be written equivalently as a particular class of a time-varying linear system. Through this suitable system representation in the form of this time-varying linear system, a numerical algorithm based on convex optimization is proposed to determine these regions of stability. Two numerical examples are given to demonstrate the effectiveness of the proposed approach...

[学科分类] 自动化工程

[关键词] Time-varying uncertain nonlinear systems ;Region of attraction ;Linear differential inclusions ;Linear matrix inequalities