International Journal of Systems Science Vol. 42, No. 10, October 2011, 1821–1830 Improved synthesis method for network-based control Fernando O. Souza a , Reinaldo M. Palhares b * and Leonardo A.B. Toˆrres b a Campus Alto Paraopeba, Federal University of Sa ˜o Joa ˜o del-Rei, Rod. MG 443 Km 7, 36420-000 Ouro Branco, MG, Brazil; b Department of Electronics Engineering, Federal University of Minas Gerais, Av. Anto ˆnio Carlos 6627, 31270-010 Belo Horizonte, MG, Brazil (Received 9 July 2009; final version received 15 January 2010) A less conservative stability analysis condition for closed-loop delayed linear systems subjected to uncertain, bounded, non-differentiable, additive time delays is presented. The obtained stability condition is applied to the problem of networked control system robust design in the presence of network-induced delays and data packet dropouts. Illustrative examples are provided to show the advantage and applicability of the developed results in this case. Keywords: time-delay systems; networked control systems; sampled-data systems; stability; linear matrix inequality 1. Introduction The control theory community has been witnessing an accelerated proliferation of control systems based on distributed sensors, actuators and controllers that exchange data through dedicated, or not, communica- tion networks. This comes as a natural consequence of ubiquitous network connectivity and the ever aug- menting computational power of dedicated devices whose cost, size and weight have been steadily decreasing for many years now (Zhang, Branicky, and Phillips 2001). A common example is the use of general purpose communication protocols, such as Ethernet TCP/IP, in industrial processes (Maciel and Ritter 1998; Yang, Chen, and Alty 2003); which greatly facilitates the integration of different levels of process automation and process information management systems. In robotics, examples are found where network- based robust control design can be useful in the implementation of networks of distributed sensors, actuators and controllers for autonomous or semi- autonomous vehicles, i.e. mobile robots. In this case, there are at least two instances that have been demanding deeper theoretical analysis of network- induced delays on closed-loop stability: (i) in the control of single robots where the diverse commercial options for sensors and actuators, in terms of output protocols, are such that the optimal tradeoff among flexibility, cost and reliability sometimes is achieved through the use of general purpose interface nodes used to connect these devices in a dedicated network, together with hard and/or soft requirements on real-time operation, despite the fact that the devices are relatively close to each other inside the robot (Wu and Hu 2008) and (ii) in the control of swarms of robots, where the communication requirements on maximum allowed delay to exchange data between units may become critical to the successful coordina- tion of multiple agents (Gu and Hu 2009). Usually, the solutions for the aforementioned problems involving network-based control systems follow the path of designing specific network hardware and/or protocols to guarantee as small as possible network-induced delays; or, on the other hand, they follow the approach of incorporating information on the unavoidable network delays in the controller synthesis procedure (Shanbin, Wang, and Sun 2002; Tipsuwan and Chow 2003; Yang 2006; Gao, Chen, and Lam 2008; He, Wang, and Zhou 2008a; He, Wu, Han, and She 2008b; Liu, Chai, Mu, and Rees 2008; Yang, Wang, and Yang 2008; Zhang and Yu 2008; Mao, Jiang, and Ding 2009; Vatanski, Georges, Aubrun, Rondeau, and Ja¨msa¨-Jounela 2009). This last alterna- tive is pursued in this article. A brief survey on networked control systems (NCS) can be found in Yang (2006), where the impact of the specific NCS problems on traditional large-scale system control methodologies is presented, together with some NCS oriented strategies used in the litera- ture, particularly on the use of Markov chain theory, (Yang et al. 2008; Liu, Ho, and Niu 2009). It is important to point out that transition probabilities of *Corresponding author. Email: palhares@cpdee.ufmg.br ISSN 0020–7721 print/ISSN 1464–5319 online ß 2011 Taylor & Francis DOI: 10.1080/00207721003653732 http://www.informaworld.com