Fault Detection of Discrete ‐ time LPV System Based on Event Triggering Mechanism

: For discrete-time linear parameter varying systems with distributed time delays, the problem of fault detection under event triggering mechanism is studied. Based on the parameter dependent Lyapunov function method, the sufficient conditions for the system to be asymptotically stable and meet the H∞ performance criterion are given. The parameter matrix of fault detection filter is obtained by solving LMI technology. In addition, the event triggering strategy is introduced to save network resources.


Introduction
As a kind of time-varying system with uncertain parameters, linear parameter variation (LPV) system has been widely used in aerospace, industrial manufacturing, wind power generation and other fields [1][2][3]. No matter in which field, the operation of the control system is inseparable from the network environment. On the one hand, due to some disadvantages of the network control system itself, on the other hand, due to the influence of external complex working conditions, various faults will appear in the operation process of the control system [4][5]. If these faults can not be found and solved in time, it will either lead to the temporary collapse of the system, affect the working process, or lead to the empty of human and financial resources. Therefore, it is very meaningful for the system to detect the fault information as soon as possible and take necessary measures before the fault occurs. However, the network control system is limited by the network bandwidth, and a large number of data will be congested in the transmission process [6][7][8]. In addition, the previous control strategy based on time trigger requires the system to sample in each cycle. If the sampling cycle interval is too small, the system will sample and send data frequently, which can not effectively filter useful information. In this regard, a new control strategy based on event triggering is introduced to make the system execute tasks under specific triggering conditions, the required information is transmitted and the useless information is filtered [9]. Based on the mode dependent switching strategy and the Lyapunov stability theory of dual dependence of parameters and modes, reference [10] studies the design of asynchronous H∞ fixed order filters for LPV time-delay switched systems under the mode dependent mean residence time method. Literature [11] gives sufficient conditions for the existence of filters for discrete LPV systems by using linear matrix inequality technology and parameter dependent quadratic Lyapunov function method. On this basis, literature [12] and literature [13] give H∞ filter design methods for parameter bounded discrete LPV systems and observer design methods for discrete LPV systems with unknown inputs respectively, The former also verifies the effectiveness of the proposed filter design scheme through a numerical simulation.

Problem Statement
Consider the following form of discrete-time switched LPV system A fault detection filter in the form of formula (2) is designed to obtain the residual signal of the system and detect the fault of the system the parameter matrix of fault detection filter to be solved.
Setting the event-triggered condition Definition 1. The switched LPV system (1) has H ∞ performance, if there exist event-triggered condition (3), filter (2) such that the following conditions are satisfied (4) is asymptotically stable.

Under the zero initial condition, for all nonzero
, the filtering error system and the control system satisfies

Main Results
For the fault detection system (4), by selecting the appropriate Lyapunov Krasinski functional, a sufficient condition is proposed to make the fault detection system (4) asymptotically stable and meet the H ∞ performance criterion under the event trigger mechanism, which provides a theoretical basis for the later design of fault detection filter.
The forward difference along the system (4) can be obtained The performance index in the form of formula (6) is introduced Under zero initial conditions, According to theorem 1, for any non-zero vector   then the fault detection system (4) is asymptotically stable, and its H ∞ performance is guaranteed.
Since the matrix ( )  k