ON THE STRUCTURAL STABILITY IN THE CONTEXT OF FILIPPOV THEORY

Abstract

The paper attempts a brief overview of the field of stability of elastic structures.
The structural stability is a fundamental property of a switched dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations. Examples of such qualitative properties are numbers of fixed points and periodic orbits.
Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations of the system itself. Variants of this notion apply to systems of ordinary differential equations, vector fields on smooth manifolds and flows generated by them. In this paper, the dynamical systems governed by piecewise smooth vector fields, are treated.