Robust stabilisation control for discrete-time networked control systems

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H 1-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method. 1. Introduction Networked control systems (NCSs) are systems in which a control loop is closed via a shared communication network. The use of a shared network in the feedback path has several advantages, including low installation cost, reducing system wiring, simple system diagnosis and easy maintenance. However, some inherent shortcomings, such as bandwidth constraints, packet delays and packet dropout, will degrade performance of NCSs or even cause instability. NCSs have received much attention during the past decade; see, for example, (2005). In the literature, stochastic approaches are typically adopted to deal with network packet dropout and to establish the stability of the NCS in the sense of mean square statistics (Ji, Chizeck, Feng, and