9783540406754

Realization Theory of Discrete-Time Dynamical Systems

by ;
  • ISBN13:

    9783540406754

  • ISBN10:

    3540406751

  • Format: Paperback
  • Copyright: 2004-02-01
  • Publisher: Springer Nature

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

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Supplemental Materials

What is included with this book?

Summary

This monograph extends Realization Theory to the discrete-time domain. It includes new results and constructs a new and very wide inclusion relation for various non-linear dynamical systems. After establishing some features of discrete-time dynamical systems it presents results concerning systems which are proposed by the authors for the first time. They introduce General Dynamical Systems, Linear Representation Systems, Affine Dynamical Systems, Pseudo Linear Systems, Almost Linear Systems and So-called Linear Systems for discrete-time and demonstrate the relationship between them and the other dynamical systems. This book is intended for graduate students and researchers who study control theory.

Table of Contents

Introduction
1(9)
Input/Output Maps
9(6)
Concatenation Monoid: Set of Experiments
9(1)
Input Response Map (Input/Output Map with Causality)
10(4)
Historical Notes and Concluding Remarks
14(1)
General Dynamical Systems
15(23)
Realization Theory of General Dynamical Systems
15(3)
Finite General Dynamical Systems
18(5)
Control Systems and Multi-experiments
23(3)
Historical Notes and Concluding Remarks
26(2)
Appendix
28(10)
U-Actions
28(2)
Pointed U-Actions
30(2)
U-Actions with a Readout Map
32(1)
General Dynamical Systems
33(5)
Linear Representation Systems
38(41)
Realization Theory of Linear Representation Systems
38(3)
Finite Dimensional Linear Representation Systems
41(7)
Partial Realization Theory of Linear Representation Systems
48(2)
Historical Notes and Concluding Remarks
50(2)
Appendix
52(27)
Realization Theorem
52(1)
Linear State Structure: Linear U-Actions
52(5)
Pointed Linear U-Actions
57(2)
Linear U-Actions with a Readout Map
59(1)
Linear Representation Systems
60(1)
Sophisticated Realization Theorem
61(3)
Finite Dimensionality
64(1)
Pointed Finite Dimensional Linear U-Actions
64(3)
Finite Dimensional Linear U-Actions with a Readout Map
67(2)
Finite Dimensional Linear Representation Systems
69(1)
Existence Criterion for Linear Representation Systems
70(1)
Realization Procedure for Linear Representation Systems
71(1)
Partial Realization
71(1)
Pointed Linear U-Actions
71(1)
Linear U-Actions with a Readout Map
72(1)
Partial Realization Problem
73(6)
Affine Dynamical Systems
79(34)
Realization Theorem of Affine Dynamical Systems
79(5)
Finite Dimensional Affine Dynamical Systems
84(7)
Historical Notes and Concluding Remarks
91(2)
Appendix
93(20)
Realization Theorem
93(1)
Fundamentals for Affine Dynamical Systems
93(1)
Affine State Structure: Linear U-Actions
94(4)
Affine State Structure with a Readout Map
98(3)
Affine Dynamical Systems
101(2)
Sophisticated Realization Theorem
103(2)
Finite Dimensionality
105(1)
Pointed Finite Dimensional Linear U-Actions
105(3)
Finite Dimensional Linear U-Actions with a Readout Map
108(2)
Finite Dimensional Affine Dynamical Systems
110(1)
Existence Criterion for Affine Dynamical Systems
111(1)
Realization Procedure for Affine Dynamical Systems
112(1)
Pseudo Linear Systems
113(43)
Input Response Maps with Time-Invariance
113(1)
Pseudo Linear Systems
114(3)
Finite Dimensional Pseudo Linear Systems
117(5)
Partial Realization of Pseudo Linear Systems
122(3)
Real-Time Partial realization of Pseudo Linear Systems
125(1)
Historical Notes and Concluding Remarks
126(2)
Appendix
128(28)
Realization Theory
128(1)
Deriving Pseudo Linear Systems from Affine Dynamical Systems
128(1)
Linear State Structure: Free Motions
129(3)
Free Motions with an Affine Map
132(3)
Free Motions with a Readout Map
135(1)
Pseudo Linear Systems
136(1)
Sophisticated Pseudo Linear Systems
137(3)
Finite Dimensionality
140(1)
Finite Dimensional Free Motions with an Affine Map
140(3)
Finite Dimensional Free Motions with a Readout Map
143(2)
Finite Dimensional Pseudo Linear Systems
145(1)
Existence Criterion for Pseudo Linear Systems
146(1)
Realization Procedure for Pseudo Linear Systems
146(1)
Partial Realization
147(1)
Free Motions with an Affine Map
147(1)
Free Motion with a Readout Map
148(1)
Partial Realization Problem
149(5)
Real-Time Partial Realization Problem
154(2)
Almost Linear Systems
156(39)
Time-Invariant, Affine Input Response Map (Input Response Maps with Time-Invariance and Affinity)
156(1)
Almost Linear Systems
157(3)
Finite Dimensional Almost Linear Systems
160(5)
Partial Realization Theory of Almost Linear Systems
165(2)
Real-Time Partial Realization Theory of Almost Linear Systems
167(2)
Historical Notes and Concluding Remarks
169(1)
Appendix
170(25)
Realization Theory
171(1)
Deriving Almost Linear Systems from Pseudo Linear Systems
171(1)
Free Motions with an Affine Map
172(4)
Free Motions with a Readout Map
176(2)
Almost Linear Systems
178(1)
Sophisticated Almost Linear Systems
179(2)
Finite Dimensionality
181(1)
Finite Dimensional Free Motions with Affine Map
181(3)
Finite Dimensional Free Motions with a Readout Map
184(2)
Finite Dimensional Almost Linear Systems
186(1)
Existence Criterion for Almost Linear Systems
187(1)
Realization Procedure for Almost Linear Systems
187(1)
Partial Realization
188(1)
Free Motions with an Affine Map
188(1)
Free Motions with a Readout Map
189(1)
Partial Realization Problem
190(4)
Real-Time Partial Realization of Almost Linear Systems
194(1)
So-Called Linear Systems (Linear Systems with a Non-zero Initial State)
195(24)
Input Output Relations for So-Called Linear Systems
196(1)
So-Called Linear Systems and Almost Linear Systems
197(6)
Partial Realization Theory of So-Called Linear Systems
203(4)
Real-Time Partial Realization Theory of So-Called Linear Systems
207(1)
Historical Notes and Concluding Remarks
208(2)
Appendix
210(9)
So-Called Linear Systems and Almost Linear Systems
210(1)
Partial Realization
211(6)
Real-Time Partial Realization
217(2)
References 219(8)
Index 227

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