Distributed control of nonstationary LPV systems over arbitrary graphs

Abstract

This paper deals with the ℓ2-induced norm control of discrete-time, nonstationary 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.