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Robust ${H}_{\infty }$-control of delayed singular systems with linear fractional parametric uncertainties. (English) Zbl 1160.93330
Summary: This paper deals with the problem of robust ${H}_{\infty }$ 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 ${H}_{\infty }$-norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the application of the proposed method.
##### MSC:
 93B36 ${H}^{\infty }$-control 93B35 Sensitivity (robustness) of control systems 15A39 Linear inequalities of matrices 93C15 Control systems governed by ODE