Packet loss compensation-based fault detection for fuzzy Markov jump systems: A zonotopic residual evaluation approach

Abstract

This paper focuses on the fault detection problem for a class of nonlinear Markov jump systems with packet losses, in which the nonlinearity and uncertainty of the original system are captured by the interval type-2 fuzzy sets. To deal with the random packet losses, a single exponential smoothing technique-based compensation scheme is introduced to counteract the effect of missing measurements. On this basis, an asynchronous fuzzy filter is designed. Then, using the residual signals generated by the filter, a zonotopic-based detection strategy is proposed to calculate dynamic thresholds and detect actuator faults. By applying the information about the footprint of uncertainty and the Lyapunov functional approach, the membership-function-dependent filter design conditions are obtained, which can guarantee the stochastic stability and strict dissipativity of the fault detection system. Compared with the membership-function-independent filtering design conditions in the existing results, the given membership-function-dependent ones reduce the conservatism of the design. Finally, a tunnel diode circuit example is provided to validate the effectiveness of the proposed approach, which shows that the zonotopic threshold analysis-based detection method shortens the fault response time more than the one using the constant threshold.