ABSTRACT

This chapter introduces a new approach (one-dimensional (ID) vectorial form) to set the stage for extending discrete-time sliding mode control (DSMC) to two-dimensional (2D) systems. Using 1D form to represent 2D systems can be used as an alternative strategy to reduce the inherent complexity of 2D systems and their applications. Unlike the Wave Advanced Model form, the suggested 1D vectorial form, in the chapter, has invariable dimension and hence a regular form of system can be derived which is the basis of DSMC here. The chapter considers the first Fornasini and Marchesini model of 2D systems which is a second order recursive form. In the proposed 1D vectorial form of the chapter, one of the 2D variables (i or j) is stacked and consequently the original 2D process is replaced by a 1D virtual process which can be controlled easily. Dealing with this new 1D form, the designing procedure of DSMC is more straightforward compared to the 2D system.