Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems

This study is concerned with the static output-feedback stabilisation problem of discrete-time networked control systems. If the controlled plant is a discrete-time system, the networked control system with time-varying network-induced delays and data packet dropouts in the transmission is modelled as a discrete-time system with time-varying delays in the state. The network-induced delays are assumed to have both an upper bound and a lower bound. Next, an asymptotic stability condition for the networked control systems is established, which depends on the upper and lower bounds of delay times. Then, three approaches to the static output-feedback controller are proposed, where the effect of both network-induced delays and data packet dropouts has been considered. Furthermore, the robust stability condition and controller design method for such networked control systems with structured uncertainties are presented. All the results are formulated in the terms of linear matrix inequalities (LMIs), which are numerically very efficiently solved via LMI toolbox in the Matlab. Finally, three examples are worked out to illustrate the feasibility and effectiveness of the proposed method.