Analysis And Design Of A Class Of Networked Control Systems With Multiple Probability Intervals Distributed Time Delay

With the rapid development and wide application of computer and network communication technology,networked control systems are more and more relevant to people’s life.Networked control systems use network to realize the communication between key modules,so that the NCSs have the advantages of remote control,easy to expand and maintain that traditional control systems do not have.However,NCSs also have problems such as network-induced delay,data packet dropout and data packet disorder.In this paper,we mainly study the influence of network-induced delay and external disturbances on NCSs,especially the probabilistic characteristics of network-induced delay.Based on Lyapunov-Krasovskii(L-K)functional,we will analyze the stability of the system and design the controller.The main research contents of this paper are as follows:(1)Study the stability of NCSs with network-induced delay.First,in order to make full use of the time delay information,a quadruple integral and an augmented matrix are introduced in the construction of L-K functional.Then,the Wirtinger integral inequality,convex combination method and Jensen integral inequality are used to deal with the integral terms from the derivation of functional,and the stability theorem with less conservativeness is given in the form of an linear matrix inequality.Finally,the correctness of the theorem is verified by comparison with the numerical examples from other literatures and Simulink simulations.(2)The stability of a class of networked control systems with three-probability interval distributed time-delay is studied.Assuming that the probability distributions of time delay in three intervals are known,first,two random variables that obey the Bernoulli distribution are introduced to characterize the probability distributions of the time delay in three intervals,and a system model with three probability interval distributed time delay is established.Second,when constructing the Lyapunov-Krasovskii functional,the augmented matrix and triple quadruple integral terms are introduced to make better use of the time delay information of the system.Then,Wirtinger integral inequality and convex combination are used to deal with the integral terms from weak infinite operation of double integral in L-K functional,and Jensen integral inequality is used to deal with the integral terms from weak infinite operation of triple integral and quadruple integral,respectively.A less conservative stability criterion is given by a sufficient condition in the form of an LMI.Finally,the validity of the stability criterion is verified by numerical examples and simulations.(3)The control problem of a class of T-S fuzzy three-probability interval distributed time-delay networked control systems is studied.First,T-S fuzzy model is used to approach a nonlinear system with network-induced delay and external disturbances.Then,three probability interval distributed time delay is introduced to establish the system model.And then,the L-K functional containing quadruple integral is constructed,and the system stability theorem is given and the controller is designed by using Schur complementary lemma and appropriate integral inequality.Finally,the upper bound of the maximum time delay and the controller gain are obtained by the LMI toolbox,and the effectiveness of the controller design is verified by Simulink simulations.