Stability of linear Markovian jump systems

The authors study the stability properties of linear Markovian jump systems and the relationship among second moment and sample path stability properties. It is shown that asymptotic mean square stability, exponential mean square stability, and stochastic stability are equivalent, and that they imply almost sure stability of the system. The relation between almost sure stability and delta -moment stability for ID jump linear systems is also examined. The Lyapunov exponent method for the study of almost sure stability is discussed, and a theorem which characterizes the qualitative properties of Lyapunov exponents of the jump linear systems is stated.<>