Robust control of delayed singular systems with linear fractional parametric uncertainties

This paper deals with the problem of robust H ∞ control for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is feasible, a desired robust state feedback control law can be constructed, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is not only regular, impulse free and stable, but also meets an H ∞ -norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the application of the proposed method.