State-space realisations of linear 2-D systems with extensions to the general nD (n[>̳]2) case - Galkowski, Krzysztof, 1949- (London ; New York : Springer, 2001)
Introduction. Preliminaries
State-space Models
Transfer Function Matrices and Polynominal Description
The Galkowski Approach - the SISO Case
Singularity. The Elementary Operation Algorithm for Polynominal Matrices
Basics
Analysis of the Elementary Operation Algorithm
The EOA and Polynominal Matrix Description
The EOA and Similarity
The Elementary Operation Algorithm and Singularity
Initial Representations for the Elementary Operation Algorithm
Relationships between the Roesser and the Fornasini-Marchesini Models. 2D Sate-space Realizations and the Elementary Operation Algorithm - the Single Input - Single Output (SISO) Case
Basics
Links between the Roesser and the Fornasini-Marchesini Models by the EOA. MIMO Systems - the 1D Case
Multi-input Single-output Systems
Single-input Multi-output Systems
MISO and SIMO Cases-the Dual Approach
General MIMO Case
Further Analysis
An Algebraic Characterization. Multiple-input, Multiple-output (MIMO) Systems - the 2D Case
The General Approach
Column Least Common Multiplicity Based Approach
Row Least Common Multiplicity Based Approach
A Standard (Nonsingular) Realization Achieved by Direct Application of the EOA
Algebraic Justification for the MIMO Case
Variable Transformations for the Elementary Operation Algorithm
Variable Inversion
Generalised Bilinear Transform. The Elementary Operation Approach Extensions
The nD Elementary Operation Algorithm
Applications to Repetitive Processes
The Elementary Operation Algorithm and Laurent Polynominals. State-Space Realizations for 2D/nD Systems Revisited - Relations to EOA
Overview
A priori Non-minimal Realization
Multi-way Companion Matrices
The History of Multi-way Matrices
Multi-way Matrices - Mathematical Basics
Three-way Companion Matrix of a Trivariate Polynominal
Minimal Realization for Multi-linear n-variate Transfer Functions. Conclusions and Further Work. References. Index.
On t.p. "[>̳]" appears as the "greater than or equal to" symbol.
Includes bibliographical references and index.
Keywords: System analysis; State-space methods; Linear systems