Max-type copositive Lyapunov functions for switching positive linear systems

The paper aims to expand the stability analysis framework based on copositive Lyapunov functions (CLFs) for arbitrarily switching positive systems with continuous- or discrete-time dynamics. The first part focuses on max-type CLFs. It provides an algebraic characterization (in terms of weak quasi-linear inequalities), as well as an existence criterion relying on a concrete construction procedure (in terms of Perron–Frobenius eigenstructure). The second part explores the connections between max-type and two other classes of CLFs, namely linear and quadratic-diagonal. New qualitative and quantitative features are revealed for the CLFs belonging to the two mentioned classes.