Research On Finite-time Fault Detection Methods For Singular Systems With Time Delays

Because of the particularity and superiority of the singular system structure,singular system can accurately describe the power system,economic system,constrained mechanical system and other systems.Singular system has been the focus of scholars since it was proposed,and has become a hot research.As an important means of troubleshooting and preventing faults,fault detection technology has always been a hot topic for researchers since it was proposed.In recent years,the problem of singular system fault detection has been concerned by scholars,and some important research achievements have been made under the efforts of scholars.However,the problem of singular system fault detection in the sense of finite time needs to be further explored.At the same time,in the current fault detection schemes of singular systems,detectors designed based on H_∞index are mostly used,and only the robustness of residual system is considered.However,as another important index to measure the performance of fault detection—fault sensitivity,there are only a few design schemes ofH_-H_∞fault detection detector considering both indexes.In this paper,the problem of finite-time fault detection for linear singular systems with time-varying delays is studied.Firstly,the design of finite time H_∞fault detection scheme for singular systems is studied.A state space filter is designed as residual generator for linear singular systems with time varying delay.Based on the Lyapuov-Krasovskii functional method,the"fast-slow"decomposition method of singular system and some algebraic techniques,the finite time stability of singular system is proved to be sufficient,and sufficient conditions are derived to ensure that the residual system is regular,impulsive,stable and satisfies the H_∞performance.The conditions given in this paper guarantee that the algebraic subsystem has the same transient performance as the differential subsystem.Then,the solvable conditions for the robust performance of fault detection filter is given in the form of linear matrix inequalities by using the variable substitution method and a series of basic operations of matrices.A numerical example of a three-machine five-bus power system is used to verify the effectiveness and applicability of the proposed scheme.Then,based on the finite time H_∞fault detection scheme of singular systems,the finite time H_-H_∞fault detection scheme of singular systems is further studied.The Lyapuov-krasovskii functional of H_∞fault detection scheme is used to analyze the newly constructed residual system,and the sufficient conditions for satisfying H_∞and H_-performance of residual system are given respectively.Then,by using the method of variable substitution and a series of basic operation of the matrix,the solvability conditions of the fault detection filter which can satisfy the disturbance rejection performance and fault sensitivity performance at the same time is given in the form of a strict linear matrix inequality.Then an optimization problem is proposed to balance the robustness of unknown disturbances and the sensitivity of faults to be checked,and an algorithm is proposed to solve the optimal filter for balancing the two indices.Finally,two numerical examples are used to analyze the parameters and compare with theH_∞fault detection scheme,which shows the effectiveness and superiority of the proposedH_-H_∞scheme.