Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 291714, 16 pages
Research Article

Mixed 𝐻 𝟐 / 𝐻 Performance Analysis and State-Feedback Control Design for Networked Systems with Fading Communication Channels

Faculty of Aerospace Engineering, University Politehnica of Bucharest, 01106 Bucharest, Romania

Received 1 July 2011; Accepted 2 September 2011

Academic Editor: Zidong Wang

Copyright © 2012 Adrian-Mihail Stoica. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 𝐻 2 / 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 𝐻 2 / 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.