H_∞Control For Large-scale Systems With Random Communication Delays

Networked control systems have been widely developed and applied in a broad range ofindustrial circles in recent years, because of the development of communication technology,computer technology and controlled technology. However, on the one hand, due to the bandwidthlimitations of the network, the measurement data in the network transmission process willinevitably be missing and time delay. On the other hand, many practical systems areinterconnected large-scale systems which are composed of multiple subsystems. These twophenomena have an inpact on the performance of the network system.In this paper, consideringon the both characteristics above-mentioned, the design of observers and controllers problem isresearched for linear discrete-time interconnected large-scale systems composed ofN subsystems under the circumstance that the measurement data are time delayed. The majorpoints of this paper are shown as follows:(1) For a class of linear discrete-time systems with the occurrence of measurement datadelays is assumed to be a Bernoulli distributed sequence with known probability.The design ofobserver-based controllers is studied.Based on the application of Lyapunov stability theory.Sufficient conditions are derived in terms of linear matrix inequality (LMI) which guarantee theexistence of closed-loop system exponentially stable in the sense of mean square and achieve theprescribed H_∞performance. By solving the LMI, the parameters of observer and controller canbe obtained. The simulation results show the effectiveness of the controllers algorithm.(2) For a class of linear discrete-time large-scale systems which are modeled asinterconnection of N subsystems.The design of state feedback controller is studied.Assuming thestate of close-loop system can be measured and the occurrence of measurement data delays is aBernoulli distributed sequence with known probability.Sufficient conditions are derived in termsof linear matrix inequality (LMI) which guarantee the existence of closed-loop systemexponentially stable in the sense of mean square and achieve the prescribed H_∞performance byutilizing Lyapunov theory. The parameters of controllers are obtained by solving the LMI. Thesimulation results show the effectiveness of the controllers algorithm.(3) For a class of linear discrete-time large-scale systems which are modeled asinterconnection of N subsystems. The design of observer-based controller is studied.Assumingthe state of close-loop system cannot be measured and the occurrence of measurement data delays is a Bernoulli distributed sequence with known probability. Sufficient conditions are derived interms of LMI for the existence of the observer-based controller, which can make closed-loopsystem exponentially stable in the sense of mean square and achieve the prescribed H_∞performance. The parameters of observers and controllers are obtained by solving the LMI. Thesimulation results show the effectiveness of the controllers algorithm.