Fuzzy model‐based fault detection for Markov jump systems

Abstract

SUMMARYThe robust fault detection filter (RFDF) design problems are studied for nonlinear stochastic time-delay Markov jump systems. By means of the Takagi-Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator are constructed. Moreover, taking into account the sensitivity to faults while guaranteeing robustness against unknown inputs, the H ∞ filtering scheme is proposed to minimize the influences of the unknown inputs and another new performance index is introduced to enhance the sensitivity to faults. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov-Krasovskii function. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as a two-objective optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences.

Robust finite-time H ∞ control of stochastic jump systems

“…The finite-time controller gain (23) are computed by LMIs (13)(14)(15)(16) by Theorem 3 using the MATLAB LMIs Toolbox [23]. With the sampling simulation time interval 10 , t s = we can get the following results.…”

“…It is appropriate to describe the dynamics subject to abrupt variation in their structures and parameters, such as sudden environment changes, subsystem switching, system noises and executor faults. In practice, the applications of MJSs are comprehensive, for instance, economic systems [11], communication systems [12], electrical power systems [13], robot manipulator system [14] and circuit systems [15], etc. The existing results about MJSs cover a large variety of problems such as stochastic Lyapunov stability [14,[16][17][18], stochastic controllability [11][12][13]19,20] and robust filtering [21,22], etc.…”

On Delay-Dependent Stability of Markov Jump Systems with Distributed Time-Delays

“…Since the pioneering work on quadratic control [17] of MJSs in the mid 1960s, such systems have regained increasing interest. As such, they are used to model economic systems [4], solar thermal receiver systems [25], communication systems [3], electrical power systems [2], robot manipulator systems [23] and circuit systems [1,15], etc. In the past decades, characterization of the reported stability issue of MJSs has been widely investigated and many results have been systematically reported [8, 13, 14, 16, 18-20, 22, 24, 26].…”

“…Consider the two-mode (i.e., M = {1, 2}) uncertain neutral MJS studied by Wang and Zhang[15]:A 01 = A 02 = 22 = 0 −1 , F 31 = F 32 = 0.…”

Fault Detection for Discrete-Time Nonlinear Impulsive Switched Systems

“…To date, there are many methods to solve the FD problem. As one of the typical methods, the FD problem is converted into a robust filtering problem; then ∞ technique is presented [5,6]. For another method, FD systems have been directly considered to be sensitive to the faults and simultaneously robust to the unknown disturbance, then the ∞ / − technique investigates this important issue [7,8].…”