Finite-Time Control for Discrete-Time Positive Systems Subject to Event-Triggered Scheme and Markov Jump Parameters

This brief investigates the finite-time control problem for discrete-time positive systems subject to event-triggered scheme and Markov jump parameters. Switching transition probability is used to extend the fixed transition probability, which is more suitable to describe the performance of Markov jump systems (MJSs). On the basis of the 1-norm, a developed event-triggered scheme is proposed to be associated with the sample signal and the actual signal. Furthermore, a linear Lyapunov function and an average dwell time approach are adopted to obtain sufficient conditions for guaranteeing stochastic finite-time stability of the underlying systems. Additionally, a matrix decomposition strategy is constructed to design a finite-time event-triggered control law such that the corresponding MJSs are positive and stochastically finite-time bounded. All conditions are proposed on the basis of linear programming. Finally, a local railway transportation model is provided to verify the practicability of the strategy.