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1

Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models

Napp Diego, Pereira Ricardo, Pinto Raquel, Rocha Paula

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

527--539

EN

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.

2

Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

Zhou L., She J., Li C., Pan C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 2

285--295

EN

This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

3

Nowe perspektywy w analizie żywności

Ulanowska A., Strączyński G.

LAB Laboratoria, Aparatura, Badania

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2012

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R. 17, nr 4

31-34

4

Wyznaczanie dodatniej realizacji na podstawie schematu zmiennych stanu liniowych układów hybrydowych

Kaczorek T., Sajewski Ł.

Pomiary Automatyka Robotyka

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2007

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R. 11, nr 2

PL

Sformułowano problem realizacji dla hybrydowych dodatnich układów dwuwymiarowych liniowych oraz zaproponowano metodę wyznaczania realizacji dodatniej dla danej transmitancji właściwej na podstawie schematu zmiennych stanu. Podano warunki wystarczające na istnienie realizacji dodatniej dla danej transmitancji właściwej. Podano również procedurę wyznaczania realizacji dodatniej, którą zilustrowano przykładem numerycznym.

EN

The realization problem for 2D positive linear hybrid systems is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive realization of a given proper transfer function are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

5

Reachability and minimum energy control of positive 2D systems with delays

Kaczorek T.

Control and Cybernetics

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2005

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Vol. 34, no 2

411-423

EN

The notion of internally positive 2D model (system) with delays is introduced. Solution of the 2D linear models with delays is derived. Necessary and sufficient conditions for the internal positivity and reachability of the models are established. The Cayley-Hamilton theorem for the 2D linear models with delays is extended. The minimum energy control for the internally positive 2D models with delays is formulated and solved.