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Fault detection for a class of nonhomogeneous Markov jump systems based on delta operator approach
The problem of fault detection for a class of nonhomogeneous Markov jump system is addressed in this article based on a delta operator approach. The system under consideration contains mode-dependent delays, nonlinearities, as well as nonhomogeneous Markov switching. Also, the delta operator provides a theoretically unified formulation of continuoustime and discrete-time systems. In addition to the stochastic H‘ performance, a new definition of stochastic H index is
introduced from the signal’s point of view, which gives a measurement of sensitivity from the residuals to the faults. Then, the fault detection scheme is proposed in which the effect of the disturbances on the residuals is minimized; meanwhile,the effect of the faults on the residuals is maximized. Subsequently, novel sufficient conditions are derived to treat this multiobjective optimization problem in a potentially less conservative framework. Especially for the sensitivity performance,a new convex condition, which includes some existing results, is obtained in terms of linear matrix inequalities. Finally, an aircraft application is given to demonstrate the effectiveness of the proposed method.
Keywords Fault detection, nonhomogeneous Markov jump system, delta operator, sensitivity
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