Two-dimensional sliding mode control of discrete-time Fornasini-Marchesini systems

This paper is concerned with the problem of discrete-time two-dimensional (2-D) sliding mode control (SMC) for Fornasini–Marchesini (FM) systems subject to exogenous nonlinear disturbances. With the introduction of the time instant and global state in the 2-D case, the discrete-time sliding surface function for 2-D systems is constructed. Then, based on the corresponding sliding mode dynamics, the solvability condition for the desired sliding surface function is derived. Subsequently, a sliding mode controller is designed to guarantee that the state trajectories can enter into a neighborhood of the specified sliding surface. Meanwhile, the stability of the 2-D sliding mode dynamics is also ensured. Finally, a simulation example is provided to illustrate the feasibility and the effectiveness of the presented new 2-D SMC design method. Different from existing results, the proposal focuses on the features of multi-dimension and the dynamics of 2-D systems, which is expected to develop a completely different SMC design approach for discrete-time 2-D systems.