Model reduction of distributed nonstationary LPV systems

Abstract

This paper is on the structure-preserving model reduction of distributed systems formed by heterogeneous, discrete-time, nonstationary linear parameter-varying subsystems interconnected over arbitrary directed graphs. The subsystems are formulated in a linear fractional transformation (LFT) framework, and a communication latency of one sampling period is considered. The balanced truncation method is extended to the class of systems of interest, and upper bounds on the ℓ2-induced norm of the resulting error system are derived. Balanced truncation suffers from conservatism since it only applies to stable systems which possess structured solutions to the generalized Lyapunov inequalities. The coprime factors reduction method is then provided as a partial remedy to this conservatism. An illustrative example is given to demonstrate the efficacy of the proposed approaches.