A periodic approach for input-delay problems: Application to network controlled systems affected by polytopic uncertainties

Abstract

This paper deals with robust stability and stabilization of linear discrete-time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic-like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed-loop model by means of a recent method based on robust control for discrete-time time-varying systems. Stability analysis and dynamic state-feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples.