International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 7, Issue 1, January 2018, ISSN: 2278 – 1323 www.ijarcet.org 62 Abstract—As human needs are increasing day by day to satisfying that technologies should also be develop. Multidimensional technology has the variety of signals which are available, to satisfy various criteria in multidimensional systems. There are few state space model structures i.e. Roesser, FM (fornasinimarchesini) first model, FM second model, Attasi model, GR model, these are discrete state space models we have been using since last few decades. These models can be used for various purposes because when we embed any system in these models, then system is represented in efficient manner there are various application for these models So in this paper purpose is to highlight more recent areas where Roesser model has been used as applications. As well as some applications in terms of stability is discussed with example. Index Terms—Roesser model; Applications of Roesser model; State space modeling I. INTRODUCTION Multidimensional systems has been continuously growing research interest area due to their applications in various important area such as image processing, Signal processing, seismographic data processing, water steam heating, DSP filters etc. [2] All the above areas are n-D systems in nature, they have more than one variable, so there can be problem like stability can be difficult to solve in n-D systems compare to 1-D system. The reason is that the fundamental theorem of algebra cannot be extended to multivariate polynomials. Several ways are commonly used to represent the operation involved in any digital processing. These methods can include transfer functions, convolution summations, and partial difference (recursive) equations. We can use above methods to solve 2-D problems i.e if we take image as example, The partial deference equation can be use to remove corrupted noise in image which is described by habibi, the model corresponds to 2-D extension of kalman filters. More ever image is best and common example of multi dimensions systems, where image properties varying along the horizontal and vertical directions, hence we can call it 2-D systems. As we can represent 1-d system, 2-D system can be represented by either transfer function models using -2D z transform models or by using state space models. [1] For modeling physical systems the desired accuracy lead to a high dynamic order, The model like Roesser (R)[1] model Fornasini-Marchesini (FM),[3,4]Givone–Roesser Manuscript received Jan, 2018. Prashant K Shah, Electronics Engineering Department, SVNIT, Surat, India, Phone/ Mobile No (GR) are best state space models which gives best results in analysis of n-D systems, Because state space model is a general powerfultool that is used to unify the research and study of n-D linear systems.FM and R are equivalent in homogeneous case. Fornasini-marchesini and Robert p .Roesser have published many literatures papers in between 1970 to 1980 related to modeling of physical system. This was trending times in researching in n-D systems modeling. In that golden decade, roesser has published new state space model in 1975 in that, he has taken image as example where a discrete model with a single coordinate in time is replaced by a model with two co-ordinates in space which are vertical and horizontal. He took circuit approach for developing state space model. Rosser model can continuous on both dimensions or mixed i.e one dimensions is continuous and other one can be discrete. R model is most general state space model among all state space models because other models like attasi ,FM model can be easily imbedded in R model that can help to use to analysis more towards nD systems. In initial time Rosser model was used in Image processing area, but then after it has been used in many applications, such as in 2-D control systems, in discrezation of partial differential equations, design of 2-D digital filters structures, in linear repetitive processes, in realization and model reduction of 2-D system and 2-D texture synthesis and classifications, iterative learning control and many more. In this paper latest applications based on Roesser model is discussed and its basic implementation summery discussed. Rosser model can be described as below , = ℎ ( , ) ( , ) , Where x is local state, x h an n-vector is horizontal state, x v an m-vector is vertical state. ℎ ( + 1, ) (, + 1) = 1 2 3 4 ℎ ( , ) ( , ) + 1 2 , , , = 1 2 ℎ (, ) (, ) + , , ( , ) is the input vector, ( , ) is the output vector and A1, A2, A3, A4, B1, B2, C, D are real matrices [1]. II. STABILITY As stability is a very important criterion for any physical system to working it properly. Test for stability is of 2-D system is exit in frequency domain. As number of dimensions are increases in systems stability of systems decreases. Roesser model is one of the best model by which we can conclude some stability criteria using different methods withRoesser model. The Roesser model and its various applications Prashant K Shah