Journal of the Franklin Institute 347 (2010) 1214–1226 On the hybrid LQ-based control design for linear networked systems Vadim Azhmyakov a,b,Ã , Rosalba Galvan-Guerra a , Alex Poznyak a a Departamento de Control Automatico, CINVESTAV, A.P. 14-740, CP 07000, Mexico D.F., Mexico b Systems and Control Theory Group, MPI for Dynamics of Complex Technical Systems, Sandtorstr. 1, D-39106 Magdeburg, Germany Received 2 December 2008; received in revised form 19 April 2010; accepted 21 May 2010 Abstract This paper addresses a problem of optimal control design associated with the linear networked control systems (NCSs). We study a class of the conventional networked systems in the presence of time delays and propose a hybrid LQ-based theoretical and computational approach to the above NCSs. In particular, we develop an explicit theoretical representation of the networked control processes by an adequate auxiliary hybrid systems. For the constructive feedback control design procedure we derive the necessary hybrid Riccati-formalism and propose an implementable solution procedure. & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. 1. Introduction The increasing complexity associated with many modern engineering applications, including control of technological processes, power electronics, autonomous robot guidance, process control in sensor-rich environments, and control of biological systems, has far-reaching implications for control system design. As an example, hybrid/switched and in general interconnected systems, interacting among themselves and remote users over some communication networks, introduce a whole new set of system-level challenges. In this situation the classic control design objectives such as optimality, stability, www.elsevier.com/locate/jfranklin 0016-0032/$32.00 & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2010.05.012 Ã Corresponding author at: Departamento de Control Automatico, CINVESTAV, A.P. 14-740, CP 07000, Mexico D.F., Mexico. Tel./fax: þ52 55 5747 3740. E-mail address: vazhmyakov@ctrl.cinvestav.mx (V. Azhmyakov).