Observers And Controllers Design For Large-sacle Systems With Uncertain Missing Measurements Probabilities

With the development of computer technology,communication technology and controlledtechnology,networked control systems have been widely applied in a broad range offields.However,owing to the introduction of the network,it’s uncertainty will inevitably be cause themissing measurements, which will lead to degrade the performance of the system or even makecontrolled system instability.On the other hand,many practical systems are interconnectedlarge–scale systems which are composed of multiple subsystems. The control not only exists inevery subsystem, also exists between each subsystem.But the random of network means theoccurrence probability of the missing measurement can not be measured precisely.In this paper, thedesign of observers and controllers is researched for a class of linear discrete–time interconnectedlarge–scale systems composed of N subsystems with missing measurements and the occurrenceprobability of the missing measurement is unknown. The major points of this paper are shown asfollows:(1) Full–dimensional state observers problem of a class of linear discrete–time systems withmissing measurements is studied. Assuming the occurrence of missing measurement data ischaracterized as a Bernoulli random binary switching sequence with an unknown conditionalprobability distribution.Full–dimensional state observers are designed to make estimated errorexponentially stable in the sense of mean square and achieve the prescribed H performance.Sufficient conditions are derived in terms of linear matrix inequality (LMI) for the existence of thestate observers, the parameters of the state observers are obtained by solving the LMI. Thesimulation results show the effectiveness of the algorithm.(2) H control problem of a class of linear discrete–time systems with missing measurements isstudied. Assuming the occurrence of missing measurement data is characterized as a Bernoullirandom binary switching sequence with an unknown conditional probability distribution. Statefeedback controllers are designed to make closed–loop system exponentially stable in the sense ofmean square and achieve the prescribedH performance. Sufficient conditions are derived in termsof linear matrix inequality (LMI) for the existence of the state feedback controllers, the parametersof state feedback controllers are obtained by solving the LMI. The simulation results show theeffectiveness of the algorithm. (3) For a class of linear discrete–time systems with the occurrence of missing measurement datais characterized as a Bernoulli random binary switching sequence with an unknown conditionalprobability distribution.Observer–based controllers are designed to make closed–loop systemexponentially stable in the sense of mean square and achieve the prescribed H performance.Sufficient conditions are derived in terms of linear matrix inequality (LMI) for the existence of thestate observers and controllers, the parameters of state observers and controllers are obtained bysolving the LMI. The simulation results show the effectiveness of the algorithm.