Admissibility Analysis And Filter Design For Singular Systems With Time Delay

Compared with regular systems,singular systems can preserve the structure of prac-tical systems more accurately,which are widely used in many practical systems.Singular systems can describe more kinds of practical systems than regular systems and it is more convenient and accurate to use singular systems for the description and characterization of many practical systems.When the dynamics of practical systems modeled by singular systems change abruptly,singular Markovian jump system can represent such systems better.At the same time,time delay generally exists in all kinds of practical systems and often brings adverse effects to the systems,such as instability,poor performance,and so on.In order to avoid the adverse effects of time delay,it is necessary to investi-gate the influence of time delay on dynamic systems.Therefore,the research on singular time-delay systems and singular time-delay Markovian jump systems is a subject of great theoretical significance and engineering value and has widely applied foreground.In this paper,based on strict linear matrix inequality(LMI)technique,the problems of admissibility analysis and filter design for singular time-delay systems and singular time-delay Markovian jump systems are studied in detail by analyzing and improving the existing methods and conclusions.The main results are summarized as follows:1.The problem of delay-dependent admissibility analysis for singular systems with a constant time delay is investigated.By employing the Jensen inequality and the Wirtinger-based inequality,new delay-dependent stability criteria are developed,respec-tively.Furthermore,in order to obtain less conservative results,a new method of con-structing Lyapunov-Krasovskii functionals(LKFs)is used.It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are re-moved.Finally,numerical examples are given to demonstrate the less conservatism of the results.2.The problem of H_? filtering for a class of singular systems with interval time-varying delays is considered.First,by combining the Wirtinger-based integral inequality with the reciprocally convex inequality,sufficient delay-range-dependent conditions are obtained to ensure that the considered singular system is admissible with H_? perfor-mance level.Then,based on a matrix transformation technique and employing several free scalars,more flexible conditions are proposed to get the desired filter.Finally,t-wo numerical examples are given to show the less conservatism and effectiveness of the results.3.The problem of exponential H_? filtering for singular Markovian jump system-s(SMJSs)with time-varying delays subject to sensor failures is dealt with.The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time-varying delay and sensor failures is mean-square exponentially admissible with a specified decay rate and simultaneously satisfies an H_? performance.First,the delay interval is partitioned into m subintervals and a novel mode-dependent stochastic LKF is constructed.By using the reciprocally convex inequality in each subin-terval,sufficient conditions of exponential H_? performance analysis are developed for the considered filtering error system.Then,based on these conditions,the existence condi-tions of the desired reliable filter are derived and the filter parameters are obtained.It should be mentioned that all the results presented here are not only dependent on the time delay,but also dependent on the decay rate and the partitioning size.Finally,two numerical examples are given to illustrate the effectiveness of the proposed methods.4.The problem of robust non-fragile H_? fault detection filtering for a class of SMJSs with time-varying delays and linear fractional parameter uncertainties is studied.In order to realize the fault detection for this kind of system,the fault detection filters design method is adopted.First,by constructing a novel mode-dependent stochastic LKF and employing integral inequality approach,sufficient delay-dependent conditions on stochastic admissibility and H_? performance analysis for the fault detection system are presented.Then,the existence conditions of the desired fault detection filter and the explicit expressions for calculating the filter parameters are established.Finally,two numerical examples are employed to show that our methods are effective.5.The problem of ?-dissipativity filtering for SMJSs with distributed delays is addressed.Sufficient delay-dependent conditions are developed for the stochastic ad-missibility and the dissipativity analysis of SMJSs with distributed delays by using an integral partitioning technique.Then,based on these conditions,both mode-dependent and mode-independent filters are designed such that the filtering error SMJSs with dis-tributed delays are stochastically stable and strictly(Q,S,R)-?-dissipative.Finally,numerical examples are given to illustrate the effectiveness of the proposed methods.