Event-triggered control of positive Markov jump systems without/with input saturation

Abstract

This paper proposes an event-triggered control for positive Markov jump systems without/with input saturation. First, an event-triggering condition is established in the form of 1-norm for positive Markov jump systems. Under the event-triggering condition, the term related to error signal between the sample state and the actual state is transformed into a form of interval uncertainty. Then, the positivity and stability of the systems are discussed by using the lower and upper bounds of interval uncertain systems, respectively. An event-triggered control law for the underlying systems is proposed by decomposing controller gain matrix into non-positive and non-negative parts. For positive Markov jump systems with input saturation, a design approach to the controller gain matrices and the corresponding controller auxiliary gain is presented. All conditions are described in terms of linear programming. Furthermore, the obtained approaches are developed for the discrete-time case. Finally, the effectiveness of the proposed design is verified via three examples.