Finite-Time Event-Triggered Stabilization for Discrete-Time Fuzzy Markov Jump Singularly Perturbed Systems

The finite-time event-triggered stabilization is studied for a class of discrete-time nonlinear Markov jump singularly perturbed models with partially unknown transition probabilities (TPs). T–S fuzzy strategy is adopted to characterize the related nonlinear Markov jump singularly perturbed models. The control objective is to make sure that the system states remain within a bounded domain during a fixed-time interval. First, a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth. On that basis, by using a new Lyapunov function, a developed finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue due to a small singular perturbation parameter. Moreover, the mode-dependent fuzzy controller gain and the event-triggered parameter are co-designed under the framework of partially unknown TPs. Finally, the feasibility of the main results is provided to verify the finite-time event-triggered control strategy.