Using guaranteed cost filters for fault detection of discrete-time stochastic distribution systems with time delays

If the measured information of a stochastic system is the stochastic distribution of the output, the stochastic system can be called a stochastic distribution one. In this paper a fault detection (FD) scheme is studied by using the guaranteed cost observer for the discrete-time stochastic distribution systems. A discrete-time nonlinear weighting model with time delays is established by using the square root B-spline expansions for the output distributions. As a result, the concerned FD problem is transformed into a conventional FD problem subjected to a discrete-time uncertain nonlinear time delayed system. To enhance the FD performance, the optimal guaranteed cost performance is applied for the FD observer design approach. For uncertain time-delayed systems, feasible criteria are obtained by means of linear matrix inequalities (LMIs). Simulations are given to show the efficiency of the proposed approaches.