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5
BINARY DYNAMIC SYSTEMS OF DISCRET AUTOMATION
Editor Doctor of Technical Sciences Professor A. V. Ushakov
CONTENTS………………………………………………………. 5
Table of Abbreviations and Symbols……………………………... 7
INTRODUCTION………………………………………………... 10
1. LINEAR BINARY DYNAMIC SYSTEMS (LBDS)
OF DISCRETE AUTOMATION……………………………......
13
1.1. Transfer Function (Matrix) Approach in Problem of LBDS
Model Representation………………………………………….
13
1.2. Vector-Matrix LBDS Model Representation Parameterized by
Discrete Time……………………………………………….....
23
1.3. The Problem of Dimension Reduction of LBDS Model Repre-
sentation……………………………………………………......
34
1.3.1. Reduction of Dimension of LBDS by Means of Numera-
tor and Denominator Modular Polynomials of Transfer
Function Divisibility………………………………………
34
1.3.2. Reduction of Dimension of LBDS by Means of Analysis
of Controllability and Observability Space of LBDS……..
38
1.4. The Similarity Conception in Theory of Linear Binary
Dynamic Systems………………………………………………
43
1.4.1. The Similarity Conception in Systematic Noise-Immune
Codes Decode Task……………………………………….
51
1.4.2. The Similarity Conception in Task of Binary Dynamic
Systems Synthesis Within Arbitrary Flip-Flop Logic…….
55
1.5. Vector-Matrix Model Representation of Linear Noise-
Immunity Encoding not parameterized by Discrete Time……..
59
1.5.1. Design of Noise-Immune Codes Matrices by Means of
Check Equations Within Coding and Decoding Processes
64
1.5.2. Design of Noise-Immune Codes Matrices by Means of
Sylvester Matrix Equation………………………………..
66
1.5.3. Design of Noise-Immune Codes
of Full-Block Systematization…………………………….
69
1.6. The Analysis of Structure of LBDS Motionless States and
Closed Loops…………………………………………………..
74
1.6.1. Motionless States of LBDS………………………………. 75
1.6.2. Closed Loops of LBDS…………………………………… 78
1.7. LBDS in Tasks of Dividing Noise-Immunity Code Transfor-
mation…………………………………………………………..
93
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