Published in IET Control Theory and Applications Received on 23rd February 2009 Revised on 5th August 2009 doi: 10.1049/iet-cta.2009.0096 ISSN 1751-8644 Robust mode delay-dependent H 1 control of discrete-time systems with random communication delays S. Chae F. Rasool S.K. Nguang A. Swain The Department of Electrical and Computer Engineering, The University of Auckland, Private Bag, 92019 Auckland, New Zealand E-mail: sk.nguang@auckland.ac.nz Abstract: This study considers stability and robust mode delay-dependent H 1 controller design for discrete-time systems with random communication delays. Communication delays between sensors and controllers are modelled by a finite state Markov process. Based on Lyapunov–Krasovskii functional, a novel methodology for designing a mode delay-dependent state feedback controller has been proposed. The authors also show that the existing delay-dependent approach is a special case of the mode delay-dependent approach proposed in this study. The mode delay-dependent controller is obtained by solving linear matrix inequality optimisation problems using the cone complementarity linearisation algorithm. The effectiveness of the proposed design methodology is verified by a numerical example. 1 Introduction Recent advances in communication networks have introduced a new field in control systems called networked control systems (NCSs) where the spatially distributed system components, such as sensors, actuators and controllers, are connected via network. This new development has fulfilled many requirements that have not been able to be met with the traditional point-to-point architecture. NCSs have achieved modularity, quick and easy maintenance and low cost because of the absence of wire connections between the system components [1–5]. However, the NCSs are challenged by numerous network constraints, such as bandwidth constraints, packet delays and packet dropout. The packet delay could potentially deteriorate the stability and control performance of the system. Since the network-induced delays are usually time varying and non-deterministic, the traditional control methodologies for delay systems [6–10] may not gain satisfactory performance for the control of NCSs. Recently, stochastic approaches are generally adopted to cope with network packet dropout and packet delays. In [11, 12], the stability robustness of NCSs is addressed, where the packet losses are modelled according to an independent and identically distributed Bernoulli distribution and the control input becomes zero when the data are lost (the so-called zero-control strategy). In [13], the delay is considered as white in nature with known probability distributions. Recently, in [1, 14–17], the Markov jump systems (MJSs) theory [18–20] is applied to NCSs, where the network delays are modelled as a Markov process. This paper aims to consider a class of uncertain discrete- time linear systems with random communication delays that exist between sensors and controllers. Markov process is used to model the communication channel where each mode in the Markov chain corresponds to the possible delays in the channel. Based on the Lyapunov– Krasovskii functional, a mode delay-dependent state feedback controller is proposed to stabilise a class of systems. This mode delay-dependent controller is obtained by solving Bilinear matrix inequalities (BMIs) using the cone complementarity linearisation algorithm. To the best of authors’ knowledge, the problem of designing a mode time delay-dependent controller has not been investigated before. Here, our approach depends on each mode delay, hence, as it is expected, the mode delay-dependent 936 IET Control Theory Appl., 2010, Vol. 4, Iss. 6, pp. 936–944 & The Institution of Engineering and Technology 2010 doi: 10.1049/iet-cta.2009.0096 www.ietdl.org