Abstract

This paper address the left invertibility problem for a special class of switched linear system. The state vector of the mentioned system is not observable at any time. Firstly, this work treated this problem with respecting the hybrid time trajectory and using the new observability concept (Z(T N )-Observability). Then, based on the state of the switching signal, two cases of hybrid observers are designed. The first one, when the switching signal is known, a hybrid observer is designed based on the finite time observer coupled with an estimator. The second one, when the switching signal or a discrete state is not available, a High Order Sliding Mode(HOSM) differentiator is designed for recovering the switching signal firstly and then recovering the continuous states. The well founded of the proposed method was highlighted by simulation work.

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