Sliding Mode Control for Uncertain 2-D FMII Systems Under Stochastic Scheduling

In this article, the sliding mode control (SMC) problem is addressed for two-dimensional (2-D) systems depicted by the second Fornasini–Marchesini (FMII) model. The communication from the controller to actuators is scheduled via a stochastic protocol modeled as Markov chain, by which only one controller node is permitted to transmit its data at each instant. A compensator for other unavailable controller nodes is introduced by means of previous transmitted signals at two most adjacent points. To characterize the features of 2-D FMII systems state recursion and stochastic scheduling protocol, a sliding function associated with the states at both the present and previous positions is constructed, and a scheduling signal-dependent SMC law is designed. By constructing token- and parameter-dependent Lyapunov functionals, both the reachability of the specified sliding surface and the uniform ultimate boundedness in the mean-square sense of the closed-loop system are analyzed and the corresponding sufficient conditions are derived. Furthermore, an optimization problem is formulated to minimize the convergent bound via searching desirable sliding matrices, meanwhile, a feasible solving procedure is provided by using the differential evolution algorithm. Finally, the proposed control scheme is further demonstrated via simulation results.