Fault detection for a class of nonhomogeneous Markov jump systems based on delta operator approach

Abstract

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 continuous-time 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.