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Gain-scheduled dynamic output feedback control for discrete-time LPV systems. (English) Zbl 1273.93076
Summary: This paper presents synthesis conditions for the design of gain-scheduled dynamic output feedback controllers for discrete-time linear parameter-varying systems. The state-space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective $$\mathcal H_{\infty }$$ and $$\mathcal H_{2}$$ gain-scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a-priori unknown, but measured in real-time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter-dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach.

##### MSC:
 93B52 Feedback control 93C55 Discrete-time control/observation systems 93B36 $$H^\infty$$-control
SeDuMi
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