On the topological entropy of continuous-time polytopic systems

Abstract

This paper investigates the topological entropy of continuous-time polytopic systems. The topological entropy is a measure that quantifies the instability in dynamical linear systems and has important applications in autonomous systems. Polytopic systems are dynamical linear systems whose coefficients are functions of an uncertain vector constrained into a polytope. A novel approach is proposed for establishing upper bounds of the largest topological entropy of continuous-time polytopic systems based on the Routh-Hurwitz stability criterion. The upper bounds are established through Linear Matrix Inequality (LMI) feasibility tests, which amount to solving convex optimization problems. A numerical example illustrates the proposed approach. Copyright (c) IARIA.