Mixed H2/H∞ Performance Analysis and State‐Feedback Control Design for Networked Systems with Fading Communication Channels

Abstract

The purpose of the present paper is to provide a performance analysis approach of networked systems with fading communication channels. For a Ricean model of the fading communication channel, it is shown that the resulting system has a hybrid structure including the continuous‐time dynamics of the networked systems and a discrete‐time dynamics of the communication channels. Moreover, this resulting hybrid system has both multiplicative and additive noise terms. The performance analysis naturally leads to an H2/H∞‐type norm evaluation for systems with finite jumps and multiplicative noise. It is proved that this norm depends on the stabilizing solution of a specific system of coupled Riccati′s equations with jumps. A state‐feedback design problem to accomplish a mixed H2/H∞ performance is also considered. A numerical iterative procedure allowing to compute the stabilizing solution of the Riccati‐type system with jumps is presented. The theoretical results are illustrated by numerical results concerning the tracking performances of a flight formation with fading communication channel. The paper ends with some concluding remarks.