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This paper addresses the observability analysis and the observer design of the continuous state for a particular class of linear switched systems. Using some dynamical properties of considered systems, we give a simple necessary and sufficient condition of the observability for a predetermined switching sequence. The obtained observability condition leads us to design a new real time state observer. This latter is based on the exact accumulation of the information provided from the switching sequence of modes, and it convergences once the observability condition is verified. Some examples with simulation show the efficiency of the obtain observability condition and the proposed state observer.