Robust fault detection for switched systems with unstable modes: A bumpless transfer piecewise filtering approach

Abstract This investigation addresses the bumpless transfer fault detection (FD) problem within switched systems that possess unstable modes. A switched piecewise FD filter is developed as a residual generator by segmenting each dwell time interval. The transition between different filters precipitates pronounced, abrupt jumps in the residual signal. Consequently, a novel definition of the residual bumpless transfer performance is introduced to constrain the magnitude of residual fluctuations during switching instances. Additionally, an alternating switching strategy—characterized by slow and fast mode‐dependent average dwell time and supported by the multiple discontinuous Lyapunov function method—is devised to assure the asymptotic stability and the weighted performance of the augmented system. Concurrently, sufficient conditions for the solvability of the bumpless transfer FD problem are articulated in the form of linear matrix inequalities. Lastly, a switched buck‐boost circuit and a numerical example are presented to substantiate the merits of the proposed bumpless transfer piecewise filtering method.