Some Notes on the Controllability, Zero-Controllability and Dead-Beat Controllable Estimator for 2D Behaviors on H0

Abstract

This article presents some observations concerning two-dimensional (2D) behaviors control problem on the discrete grid H0. Firstly, controllability and zero-controllability of 2D behaviors on H0 are characterized. Two properties of 2D sub-behaviors on H0 are introduced and investigated in order to consider controllability and zero-controllability of latent variables in 2D system, and then used to investigate 2D Roesser model which has controllability and zero-controllability. Next, equivalent systems (ESs) are defined to represent two systems that have same behaviors, their property of maintaining controllability and zero-controllability is revealed. Such equivalence is then applied to find the simple form of controlled juxtaposition systems. Finally, issues on dead-beat controllable estimator behaviors are studied, such as the relationship between zero-controllable behavior and dead-beat controllable estimator behavior, the existence of dead-beat controllable estimator behavior, etc.