Hybrid dynamic event-triggered fault control of positive Markovian jump systems

This paper presents a new hybrid dynamic event-triggered control framework on positive Markovian jump systems in continuous- and discrete-time contexts subject to actuator fault. First, a new hybrid dynamic event-triggering mechanism consists of two types of conditions: One is a dynamic event-triggering condition associated to dynamic variable and the other one is a static event-triggering condition. Under the new triggering mechanism, an interval approach is introduced to assist the control design, for which the lower and upper bounds of the original system are obtained. A nonfragile controller is proposed for stochastic stability of the underlying continuous-time system with actuator fault by virtue of stochastic copositive Lyapunov functions. Under the designed controller, the positivity and stability of the system are achieved by guaranteeing the positivity and stability of the lower and upper bound systems, respectively. Moreover, a hybrid dynamic event-triggered mechanism is established for discrete-time systems. A nonfragile hybrid dynamic event-triggered control is explored for discrete-time positive Markovian jump systems. All the conditions can be solved by linear programming. Finally, two examples are given to verify the validity of the proposed design.