Stochastic Stability of Semi-Markov Jump Linear Systems: An LMI Approach

The semi-Markov jump linear system is more general than the classic Markov jump linear system. In the semi-Markov jump linear systems, the governing stochastic process is not a Markov process, but a semi-Markov process. Instead of the exponential distribution for the sojourn-time in each mode in the jump linear system, the Weibull distribution is considered in this paper. By deriving the infinitesimal generator for the Lyapunov function of the semi-Markov jump linear system, the numerically testable sufficient conditions for stochastic stability of semi-Markov jump linear systems are obtained. Numerical examples are provided to validate the proposed sufficient stochastic stability conditions.