Stability of Delayed Systems Modeled by Fractional Models

This paper discusses linear fractional representations (LFR) of parameter-dependent nonlinear systems with real-rational nonlinearities and point-delayed dynamics. Sufficient conditions for robust global asymptotic stability both independent of and dependent on the delays are investigated via linear matrix inequalities. Such inequalities are obtained from the values of the time-derivatives of appropriate Lyapunov functions at all the vertices of the polytope which contains the parametrized uncertainties.