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Zbl 1160.93330
Zhou, Shaosheng; Zheng, Wei Xing
Robust $H_\infty$-control of delayed singular systems with linear fractional parametric uncertainties.
(English)
[J] J. Franklin Inst. 346, No. 2, 147-158 (2009). ISSN 0016-0032; ISSN 1879-2693/e

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 2000:
*93B36 $H^\infty$-control
93B35 Sensitivity (robustness) of control systems
15A39 Linear inequalities
93C15 Control systems governed by ODE

Keywords: continuous singular systems; linear fractional uncertainty; linear matrix inequality (LMI); $H_{\infty }$-control; time-delay

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