Stochastic stabilization of semi-Markov jump systems with linear fraction uncertainty: State feedback case

In this note, we propose the robust state feedback control problem and the robust stochastic stability for the Semi-Markov jump linear system (S-MJLS) with the feature of Linear Fraction uncertainties. The transition rates of the S-MJLS is time varying function with respect to dwell-time d. Under the assumption that the transition rates of the S-MJLS is bounded, sufficient condition of numerical solution for the stochastic robust stability and robust state feedback control of such uncertain S-MJLS is established according to linear matrix inequalities. In order to decrease the conservativeness, the stochastic robust stability condition and robust state feedback controller is correspondingly developed via partitioning the lower and upper bounds of the time-varying transition rate, respectively. Finally, numerical simulation and comparative studies demonstrate the effectiveness and advantages of the obtained theoretical results.