Robust H_? Filtering For Singular Time Delay Systems

When modeling multi-level,multi-objective,and multi-dimensional complex systems such as mechanical systems,power systems,and aerospace systems.Conventional complete state systems can not be used to describe such complex systems.Singular systems coupled by differential equations and algebraic equations,with static and dynamic constraints on physical objects.In recent years,scholars have made many valuable results in the study of singular time-delay systems using Lyapunov function and linear matrix inequalities.In this paper,aiming at the robust H_?filtering problem of singular time-delay systems,by selecting a suitable Lyapunov function and using linear matrix inequalities,the analysis method combines the time-delay subsection method and free weight matrix to find the singular time-delay systems to satisfy the H_?performance stable sufficient conditions and carry out filter design.Firstly,when the singular systems have inter-cell time lag,by selecting the Lyapunov function and integrating the integral inequality,the H_?performance analysis of the inter-cell singular systems with time delay is carried out,and the H_?filter is designed accordingly.When the singular systems has a large interval time delay:dividing the time delay interval into two sections,fully consider the endpoint information of the interval,selecting the Lyapunov function,using the free weight matrix,analyzing the change of the Lyapunov function in each time delay period.This design H_?filter for the filters obtained by the two methods,given the same systems parameters and disturbances,the filter matrix is the only variable to illustrate the effectiveness of the time-delay subsection analysis method in reducing the conservative problem of singular time-delay systems.Secondly,when the singular systems have a large interval time delay,in order to weaken the influence of the small probability interval on the systems performance,the Bernoulli distribution is introduced.By selecting the Lyapunov functional and combining the free weight matrix,the filter error systems is guaranteed to be mean square asymptotically stable.On the basis of this stability condition and using the variable substitution method,the function matrix is decoupled and solved by the linear matrix inequalities toolbox.The example of the simulation shows the effectiveness of this design method.Thirdly,the problem of H_?filter with Markov jump singular time-delay systems is studied.The systems is a complex systems in which several subsystems jump according to random jump rules.On the basis of considering the time-delay information,combined with the time-delay division section,free weight matrix and other methods,proposed that the filter error systems is stochastically stable and meets the H_?performance index of the filter has sufficient conditions,using the variable replacement method to decouple the function matrix,solved by the linear matrix inequalities toolbox,simulation examples show the design effectiveness of the method.Finally,for the singular time-delay systems described by the T-S fuzzy model,the time-delay subsection analysis method is used to design the filter.The T-S fuzzy model describes a nonlinear systems as being approximated by multiple local linear systems according to certain fuzzy rules.Accordingly,when the filter is designed,the design is also carried out according to the corresponding fuzzy rules,and the time delay segment is added.Analysis by solving the linear matrix inequality,the filter parameters of the singular systems are obtained.A simulation example proves the effectiveness of the filter.