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Distributed control of nonstationary LPV systems over arbitrary graphs. (English) Zbl 1375.93048
Summary: This paper deals with the $$\ell_2$$-induced norm control of discrete-time, Non-Stationary Linear Parameter-Varying (NSLPV) subsystems, represented in a Linear Fractional Transformation (LFT) framework and interconnected over arbitrary directed graphs. Communication between the subsystems is subjected to a one-step time-delay. NSLPV models have state-space matrix-valued functions with explicit dependence on time-varying terms that are known a-priori, as well as parameters that are not known a-priori but are available for measurement at each discrete time-step. The sought controller has the same interconnection and LFT structures as the plant. Convex analysis and synthesis results are derived using a parameter-independent Lyapunov function. These conditions are infinite dimensional in general, but become finite-dimensional in the case of eventually time-periodic subsystems interconnected over finite graphs. The method is applied to an illustrative example.

##### MSC:
 93B50 Synthesis problems 93A14 Decentralized systems 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93D30 Lyapunov and storage functions
SDPT3; YALMIP
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