Modeling And Robust Control For Networked Control Systems With Time-varying Delays Based On Nominal Point Technique

In the past twenty years,more and more scholars have been attracted into the research for networked control systems(NCSs)with the rapid development of con-trol,computer,network and communication technology.Compared with traditional point to point control systems,NCSs have many advantages,such as low weight,easy installation and maintenance and high reliability.Because systems exchange the sampling data and the controller signals through real-time networks in NCSs,networked-induced delays are unavoidable.The existence of delays not only reduces the performance of the system but also can destroy the stability of the system.Therefore,it is very necessary to find the relationship between the delay bounds and the stability of the system.There always exist errors between the system model and the practical system.In addition,the working condition of the system is usually quite complicated.Therefore,it is very significant to research the system robust-ness.First,this thesis investigates the stability of NCSs with short time-varying delays(STVDs)based on the multiple nominal point technique(MNPT).The re-lationship between the stability of the system and the delay bounds is established,and the stability region of the NCS is given.Second,this thesis is concerned with non-fragile robust control problems for a class of nonlinear NCSs with time-varying delays and randomly occurring uncertainties via the nominal point technique.Final-ly,numerical examples are given to show the effectiveness of the proposed methods and obtained results.The main contents are listed as follows:(1)New stability criteria and stabilization methods on NCSs with STVDs are pro-posed.A NCS with STVDs is transformed into a time-varying discrete time system.And then,this discrete time system is converted into a equivalent time-invariant system with norm-bounded uncertainties by using robust con-trol techniques.Using this method,the conservativeness of the stability condi-tion caused by STVDs can be reduced.Based on that,a single norm-bounded uncertainty is replaced by N norm-bounded uncertainties to further reduce the conservativeness.Theoretical analysis shows that when N is increased,the stability condition becomes less conservative.For a fixed sampling peri-od,the obtained stability conditions explicitly depend on the upper and lower bounds of the time-delay.The existence condition and design method for the controllers are also presented.(2)The design problem of optimal robust non-fragile H? state feedback controller for NCSs with STVDs and controller gain fluctuation is dealt with.First,a new method is presented,according to which the NCS with STVDs is transformed into a discrete linear system with uncertain parameters.Second,considering the controller gain fluctuation,with the linear matrix inequality(LMI)tech-nique,we design a robust non-fragile state feedback controller for the system without external disturbance.Third,considering the system with external dis-turbance,a suboptimal and an optimal robust non-fragile H? state feedback controllers are designed.(3)Based on the MNPT,the problems of BIBO stability and BIBO stabilization for NCSs with STVDs are researched,and some improved results are obtained.Using the single nominal point technique,a NCS with STVDs is modeled as a time-varying uncertain discrete system,in which the uncertain parameters are norm bounded and with one nominal point.Applying the small gain theorem to this model,an improved BIBO stability criterion of the NCS is obtained.To further reduce the conservativeness arising from STVDs,the uncertain parameters are modeled as N norm bounded uncertainties based on the MNPT.The presented stability criteria depend on the bounds of STVDs.Furthermore,the controller design methods are also provided.(4)The non-fragile robust control problem for a class of nonlinear NCSs with long time-varying delay is investigated.Both the uncertain nonlinearity and the controller gain fluctuation enter into the system in random ways,and such ran-domly occurring nonlinearity(RON)and randomly occurring controller gain fluctuation(ROCGF)obey certain mutually uncorrelated Bernoulli distribut-ed white noise sequences.A new time-varying discrete time system model is proposed to describe the NCS.To reduce conservativeness arising from mod-eling time-varying parts,the time-varying parts due to the time-varying delay are treated as a norm bounded uncertainty with one nominal point using ro-bust control techniques.Based on the obtained uncertain system model,a regular and an optimal sufficient non-fragile controllers are derived by apply-ing the Lyapunov stability theory and the LMI technique,which render the closed-loop NCS to be asymptotically stable and guarantee an upper bound of the given performance cost for all admissible uncertainties.Moreover,the ex-istence condition and design method for the non-fragile stabilizing controllers are also presented.(5)Non-fragile exponential H? control problems for a class of uncertain nonlinear NCSs with randomly occurring information,such as the controller gain fluctu-ation and the uncertain nonlinearity,and STVDs,are investigated via output feedback controller.Using the nominal point technique,the NCS is converted into a novel time-varying discrete time model with norm-bounded uncertain parameters for reducing the conservativeness.Based on LMI framework and output feedback control strategy,design methods for general and optimal non-fragile exponential H? controllers are presented-Meanwhile,these control laws can still be applied to linear NCSs and general fragile control NCSs while introducing random variables.