Robust stability analysis and dynamic gain-scheduled controller design for point time-delay systems with parametrical uncertainties

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 independent of the delays and the existence of a robust stabilizing gain-scheduled dynamic controller 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. The synthesized stabilizing controller consists of an interpolation being performed with the stabilizing controllers at the set of vertices of a certain polytope where the nonlinear-rational parametrization belongs to. Some extensions are also given concerning robust global asymptotic stability dependent of the delays. Numerical examples corroborate the usefulness of the proposed formalism and its applicability to practical related problems.