Robust Filtering For Neutral Systems With Distributed Delays

In a variety of practical engineering systems,there are a lot of time delay phenomena,for example,signal processing,networked control system,belt transmission and so on.The emergence of time delays often results in system instability and performance deteriorated.At the same time,it increases the difficulty of system analysis and synthesis.Therefore,the analysis of the influence of time delays on the system,and use or reduction of this effect has been a hot issue.In recent years,as an important field of time delay systems,neutral delay systems have been widely investigated because they can describe the system state delay and the state derivative delay simultaneously.Distributed delays will appear in such circumstances when the number of delay summation terms in a system equation is increased and the differences between parameter values in neighbouring are decreased,such as the modeling of fluid propellant combustion process in rocket engine and thermal processing of materials,which consider uneven delays.From an objective point of view,distributed delays can describe the system more profoundly and accurately,revealing the nature of things change.Consequently,it is of great practical significance to study the neutral systems with distributed delays.In addition,it is also necessary to consider the influence of the uncertainty on the system caused by the mathematical modeling error,the condition changes and the external disturbance.In this paper,the problems of robust filtering for uncertain neutral systems with distributed delays are studied,and the simulation results show that the methods proposed in this paper is feasible and effective.Firstly,the problems of robust H_? and L₂ -L_? filtering for a class of uncertain neutral time-delay systems with mixed delays have been investigated.The mixed delays arise in both states and outputs are generalized by combining discrete delays and distributed delays.The uncertainties in the system are assumed to be time-varying and norm bounded.By constructing the appropriate Lyapunov function and combining with the integral inequality technique,the delay dependent sufficient conditions for the existence of the filters,which satisfying the corresponding performance index are established to guarantees that the filtering error systems are asymptotically stable.According to the obtained criteria,by employing variable substitution method,the filters are designed in the form of linear matrix inequalities.Numerical examples are provided to illustrate the effectiveness of the proposed method.Secondly,the problems of robust H_? and L₂ -L_? filtering for uncertain neutral systems with distributed delays and Markov jump parameters have been studied respectively.By establishing mode-dependent Lyapunov function,utilizing Ito differential rule and Newton-Leibniz formula,the sufficient conditions for the existence of the filters are derived such that the filtering error systems are stochastically stable with the corresponding performance constraint.The decoupling between Lyapunov function matrix and system matrix is realized by the method of matrix transformation and so on,and then the parametersof the filter are obtained by solving the convex optimization problem of linear matrix inequalities.The simulation results show that the designed filter is less conservative.Finally,the problems of designing robust H_? and L₂ -L_? filters for nonlinear neutral systems with infinite distributed delays have been researched.The nonlinearity in the system is bound by the Lipschitz condition.Based on Lyapunov function method,the Cauchy inequality is introduced to deal with the infinite distributed delay term,considering full information of time delays and using the integral inequality method,the nonlinear conditions are transformed into linear conditions,then the filter design methods are given which are easier to solve.The proposed filters can not only ensure that the filtering error systems are asymptotically stable,but also satisfy the corresponding level of disturbance attenuation.The numerical examples have demonstrated that the designed filter can restore the original system state very well and reduce the influence of unknown interference.