Stability over finite domains of 2D-systems

In this paper we investigate the stabilization over a finite region of two-dimensional (2D)-systems. Such class of systems plays an important role in the biomedical engineering context, with particular reference to the field of image processing. Often 2D-systems are defined over a finite domain of the plane, where each independent variable attains values into a given interval (for example they represent the coordinates of the pixels of a given image). On the basis of these considerations, it is quite straightforward the idea to exploit for 2D-systems the finite-time stability (FTS) theory developed in the context of the classical one-dimensional system framework. Indeed the FTS approach is a more practical concept than classical Lyapunov asymptotic stability, useful to study the behaviour of a system within a finite (possibly short) interval, and therefore it finds application whenever it is desired that the state variables do not exceed a given threshold during the transients.