Multidimensional control systems: case studies in design and evaluation

Abstract

Multidimensional control systems have been the subject of much productive research over more than three decades. In contrast to standard control systems, there has been much less reported on applications where the multidimensional setting is the only possible setting for design or produces implementations that perform to at least the same level. This paper addresses the latter area where case studies focusing on control law design and evaluation, including experimental results in one case, are reported. These demonstrate that movement towards the actual deployment of multidimensional control systems is increasing.

New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

“…The possible extensions of the presented ideas to the problems of iterative learning control [1], H filtering [12], 2-D dissipative control and filtering [14,59], robust overflow stabilization [60], etc. demand further investigation.…”

“…The knowledge of 2-D systems is very important to deal with the problems in various areas such as image data processing and transmission [2], process of gas filtration [3], energy exchanging process and electricity transmission, thermal processes in chemical reactors [4], river pollution modeling [5], grid-based wireless sensor networks [6], 2-D digital filtering [7][8][9][10][11][12][13][14], 2-D digital control systems [1,[14][15][16][17][18][19][20][21], 2-D discrete switched systems [18,19,22] etc. The subject of 2-D uncertain systems has also received a significant amount of attention [11,16,17,23].…”

Output Information Based Fault-Tolerant Iterative Learning Control for Dual-Rate Sampling Process with Disturbances and Output Delay

“…Based on an abstract model in a Banach space setting, repetitive process is a particular subclass of 2D system that operates over a subset of the upper right quadrant of the 2D plane and is characterized by a series of sweeps, or passes, through a set of dynamics defined over a finite duration known as the pass length. It is a nature setting for ILC analysis and design; the main advantage is that it gives a systematic way to simultaneously consider behaviour along the time axis and from trial to trial [23]. A detailed treatment of the dynamics of these processes, including their origins in the modeling of mining operations, can be found in [24].…”

A fast numerical test of multivariate polynomial positiveness with applications

“…Multidimensional (n-D) systems are a very active topic in the last decades with applications in many areas and, as it was stated by [28], the n-D systems approach does bring advantages in solving control problems. The n-D systems can be used to formulate a large number of problems in, e. g., digital image processing, biomedicine, and control of systems described by partial differential equations.…”