scholarly journals Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models

2019 ◽  
Vol 29 (3) ◽  
pp. 527-539
Author(s):  
Diego Napp ◽  
Ricardo Pereira ◽  
Raquel Pinto ◽  
Paula Rocha
Keyword(s):  
State Space ◽  
Necessary Conditions ◽  
Convolutional Codes ◽  
Space Representation ◽  
Realization Problem ◽  
One Dimensional ◽  
Minimal State ◽  
State Space Representation ◽  
Roesser Models ◽  
Time Invariant

Abstract It is well known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with the literature on one-dimensional (1D) time-invariant convolutional codes, there exist relatively few results on the realization problem for time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimality and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.

scholarly journals Minimal State-Space Representation of Convolutional Product Codes

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1410
Author(s):  
Joan-Josep Climent ◽  
Diego Napp ◽  
Raquel Pinto ◽  
Verónica Requena
Keyword(s):  
State Space ◽  
Convolutional Codes ◽  
Space Representation ◽  
Product Codes ◽  
Product Code ◽  
Minimal State ◽  
Systematic Procedure ◽  
State Space Representation ◽  
Minimal Dimension ◽  
Study Product

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

scholarly journals On Bumps and Reduction of Switching Transients in Multicontroller Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
Joseph J. Yamé ◽  
Michel Kinnaert
Keyword(s):  
State Space ◽  
Closed Loop ◽  
Open Loop ◽  
Space Representation ◽  
Control Loop ◽  
Minimal State ◽  
State Space Representation ◽  
Common Memory ◽  
Linear Controllers

This paper is concerned with the realization and implementation of multicontroller systems, consisting of several linear controllers, subject to the bump phenomenon which occurs when switching between one controller acting in closed loop and another controller in the set of “offline” controllers waiting to take over the control loop. Based on a deep characterization of the bump phenomenon, the paper gives a novel and simple parameterization of such set of linear controllers, possibly having different state dimensions, to cope with bumps and their undesirable transients in switched-mode systems. The proposed technique is based on a non minimal state-space representation allowing a common memory and a unique dynamics shared by all controllers in that set. It also makes each initially open-loop unstable controller run in a stable way regardless of whether that controller is connected to the controlled process.

A Dynamic Systems Model for Gasifier in IGCC

2008 ◽  
Author(s):  
Mohit Aggarwal ◽  
B. Erik Ydstie ◽  
Lee R. White
Keyword(s):  
State Space ◽  
Dynamic Systems ◽  
Process Analysis ◽  
Main Idea ◽  
Space Representation ◽  
Level Control ◽  
Minimal State ◽  
State Space Representation ◽  
Systems Model ◽  
Shrinking Core

We combine the concepts of element mole balance, population balance and shrinking core mechanism to develop a dynamic systems model for the Gasifier in an IGCC process. There is need for such a model for process analysis, optimization and low level control studies. The main idea is to use invariants, like elements (atoms), instead of compounds. This reduces the size of state space and we are able to explore the idea of a minimal state space representation for a thermodynamic process. The idea of a minimal state plays an important role in control theory as it is closely related to the concepts of controllability and observability.

scholarly journals Time History Analysis of Frame Structure Systems by State-space Representation Method

2020 ◽  
Vol 10 (1) ◽  
pp. 140-147
Author(s):  
Barham H. Ali ◽  
Brwa A. Saeed ◽  
Twana A. Hussein
Keyword(s):  
Dynamic Analysis ◽  
State Space ◽  
Linear Time ◽  
Time History ◽  
Equation Of Motion ◽  
Space Representation ◽  
State Space Representation ◽  
History Analysis ◽  
Linear Differential ◽  
Time Invariant

This paper develops the state-space representation (SSR) in the field of seismic analysis of the building structures. Dynamic analysis of multi-degree-of-freedom structures involves the solution of second-order linear differential equations which they represent the equation of motion of the structure. In this paper, a SSR was formulated to replace differential equation with two coupled first-order linear differential equations. The objectives of this study are as follows: (i) To implement the SSR as a powerful tool in dynamic analysis of frame structures and (ii) to conduct a linear time history analysis for large structures subjected to ground acceleration and the seismic responses of the building were studied as well. The analysis was based on the assumption that the system is elastic linear time-invariant system and material nonlinearity is not considered. The 1940 El-Centro earthquake time history record has been used in the study. There are many effective traditional methods which can be used for carrying out linear dynamic analysis of the structures, however, this paper introduces a state-space model as an alternative approach to perform this analysis. The advantage of this method, it works properly with MATLAB software, gives explicit result for time-invariant systems, applied to multi-input and multi-output control systems, solve the equation of motion for complicated dynamic problems.

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