Constructing the Singular Roesser State-Space Model Description of 3D Spatio-Temporal Dynamics From the Polynomial System Matrix

Mohamed S Boudellioua,Krzysztof Galkowski,Bartlomiej Sulikowski,Eric Rogers

doi:10.1109/access.2021.3065747

Mohamed S Boudellioua, Krzysztof Galkowski + Show 2 more

Open Access

https://doi.org/10.1109/access.2021.3065747

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 9	License type: CC BY 4.0

Affiliation: University of Southampton

Abstract

This paper considers systems theoretic properties of linear systems defined in terms of spatial and temporal indeterminates. These include physical applications where one of the indeterminates is of finite duration. In some cases, a singular Roesser state-space model representation of the dynamics has found use in characterizing systems theoretic properties. The representation of the dynamics of many linear systems is obtained in terms of transform variables and a polynomial system matrix representation. This paper develops a direct method for constructing the singular Roesser state-space realization from the system matrix description for 3D systems such that relevant properties are retained. Since this method developed relies on basic linear algebra operations, it may be highly effective from the computational standpoint. In particular, spatially interconnected systems of the form of the ladder circuits are considered as the example. This application confirms the usefulness and effectiveness of the proposed method independently of the system spatial order.

Highlights

This paper considers linear systems described in terms of spatial and temporal indeterminates, which belong to the general class of nD, n > 1, linear systems
Transformations between model representations are standard in analysis and controller design
This paper addresses the problem of transforming a system matrix of a 3D linear system to a singular, 3D Roesser [19] state-space model for examples where there are spatial and temporal indeterminates

Summary

INTRODUCTION

This paper considers linear systems described in terms of spatial and temporal indeterminates, which belong to the general class of nD, n > 1, linear systems. Transformations between model representations are standard in analysis and controller design This general area is more involved and less well developed for nD linear systems, for which this paper gives new results. Boudellioua et al.: Constructing Singular Roesser State-Space Model Description of 3D Spatio-Temporal Dynamics system matrix. The starting point is the so-called multivariate polynomial system matrix, which can be directly obtained for a given multidimensional system, e.g., the homogeneous, spatially distributed electrical system used to demonstrate the new results in this paper. This paper addresses the problem of transforming a system matrix of a 3D linear system to a singular (where in many cases, nonsingular models do not exist), 3D Roesser [19] state-space model for examples where there are spatial and temporal indeterminates.

PRELIMINARIES

CASE STUDY

CONCLUSION