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

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 $H_{\infty }$ 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.