Robust H∞ control for continuous descriptor systems with state delay and parametric uncertainty

The problem of robust H∞ control of delayed descriptor systems with parametric uncertainties is investigated in this paper by using a strict linear matrix inequality (LMI) design approach. It is assumed that the parametric uncertainties are of a linear fractional form, which can describe a class of rotational nonlinearities.It is shown that a desired robust state feedback control law can be constructed, given the feasibility of the LMI.The constructed control law 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. The effectiveness of the developed approach is illustrated via a numerical example.