H∞ control for a class of non-linear discrete-time networked systems with limited information

Abstract

In this article, the problems of stabilization and H ∞ control are investigated for a class of non-linear networked systems with packet dropouts, network-induced delays and sensor faults. We construct a novel model by taking packet dropouts, distributed delays and sensor faults into account in a unified way. The packet dropouts process is modelled as a Markov chain taking values in a finite state space. Network-induced delays with distributed characteristics are divided into two intervals satisfying the Bernoulli random distribution. Sensor faults are described as stochastic variables and each sensor has different fault rate and independent of others. The resulting closed-loop system is converted into a Markov switching system. A mode-dependent controller is designed such that the closed-loop system is stochastically stable and satisfies H ∞ disturbance attenuation level in terms of certain linear matrix inequalities. Finally, a numerical example is given to illustrate the usefulness of the developed method in this article. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.