1-D models for m-D processes

Controllability analysis of the first FM model of 2D systems: A row (column) process

“…Authors of [5] are the first investigators who have considered 2D systems as a 1D model. In this model, by using a different classification on local state vectors of a 2D system, a novel form of local state vectors is achieved.…”

“…However, as mentioned, this proposed form has varying dimension of states, and coefficient matrices should be updated at each step. To resolve the varying dimension of state vectors in WAM model, in [5] it is suggested to expand all states to the largest dimension via augmenting system matrices with appropriate blocks of zeros. However, the system matrices are still left varying and complicated to compute.…”

“…A different technique to deal with 2D systems is to transfer the underlying 2D system to 1D form. Wave advance model (WAM) is a 1D form of 2D systems established by [5]. In WAM model, the 2D systems are considered as advanced waves and consequently the original stationary 2D system is converted to a time varying 1D system.…”

A new approach to applying discrete sliding mode control to 2D systems

“…Porter and Aravena were the first investigators who considered 2D systems as a 1D model in 1984 [19]. In this model, by using a different classification on local state vectors of a 2D system, a novel form of local state vectors is achieved.…”

“…As another method to deal with 2D systems, it appears that the popular strategy is to generalize 1D concept. Wave advance model (WAM) is a 1D form of 2D systems established by Porter-Aravena [19]. In this method, the 2D systems are considered as advanced waves and consequently the original stationary 2D system is converted to a time varying 1D system.…”