Security control of positive semi-Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourn-time distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.