Robust Observer Design for Linear Switched Systems Based on Structural Observability Conditions

An observer, based on the well-known structural conditions of state and mode observability for switched linear systems, using a high-order sliding-mode (HOSM) differentiator, is proposed to recover both the active mode and the continuous state in Finite-time. The estimation of both the mode and the state is ensured, under some mild additional conditions, even for the case when the measurable output is affected by perturbations. Moreover, a continuous state observer for the case when the mode is unobservable, or the mode estimation is negligible, is presented considering some more relaxed structural conditions ensuring the continuous state estimation disregarding the mode.