Positive real synthesis of networked control system: An LMI approach

This paper presents positive real synthesis for Networked Control Systems (NCS) in discrete-time to render closed-loop positive realness (passivity). The synthesis is based on the definition of passivity for discrete Markovian jump linear systems, whose sufficient condition is given by stochastic Lyapunov functional. The controller via state feedback is designed to guarantee the stability of NCS and closed-loop positive realness by taking into account packet losses. A periodic communication scheme is utilized among sensor, controller and actuator. It is shown that a mode-dependent positive real controller exists if a set of coupled linear matrix inequalities have positive definite solutions. The controller can then be constructed in terms of the solutions. A numerical example is presented to show how the desired passivity performance of NCS is achieved.