The present work deals with the study of the almost sure stability of discrete-time Markov jump linear systems (MJLS). First, the stability of linear systems in discrete time (MJLS with a single mode) is introduced by the Lyapunov exponent. Then the extension of this theory to the general case is approached: a variant of Birkhoff’sergodic theorem is used to revise the equality (4.6) for the Lyapunov exponent described in [6], from this we obtain the characterization of the almost sure stability of the MJLS.

The present work deals with the study of the almost sure stability of discrete-time Markov jump linear systems (MJLS). First, the stability of linear systems in discrete time (MJLS with a single mode) is introduced by the Lyapunov exponent. Then the extension of this theory to the general case is approached: a variant of Birkhoff’sergodic theorem is used to revise the equality (4.6) for the Lyapunov exponent described in [6], from this we obtain the characterization of the almost sure stability of the MJLS.