Homogeneous polynomial Lyapunov functions for robust local synchronisation with time-varying uncertainties

This study studies robust local synchronisation in multi-agent systems with time-varying parametric uncertainties constrained in a polytope. In contrast to the existing methods with non-convex conditions via using quadratic Lyapunov function, a new criteria is proposed based on using homogeneous polynomial Lyapunov functions where the original system is suitably approximated by an uncertain polytopic system. Furthermore, the corresponding tractable conditions of linear matrix inequalities have been provided by exploiting the squares matrix representation. Then, the polytopic synchronisation margin problem is, for the first time, proposed and investigated via handling generalised eigenvalue problems. Lastly, numerical examples illustrate the usefulness of the proposed method.