Monografia zawiera nowe geometryczne podejście do analizy zer wielowymiarowych układów liniowych standardowych i singularnych. Zaproponowaną charakteryzację zer oparto na informacji zawartej w pierwszym niezerowym parametrze Markova układu. Wprowadzono nową definicję zer inwariantnych rozszerzającą dotychczasowe pojęcie zer Smitha.
Spis treści:
1. Introduction
1.1. Smith Zeros
1.2. Scope of the Book
1.3. Glossary of Symbols
2. Zeros and Output-Zeroing Problem
2.1. Definitions of Zeros
2.2. Decoupling Zeros
2.3. Invariant Zeros and Transmission Zeros
2.4. Output-Zeroing Problem
2.5. Relationship between Smith Zeros and Invariant Zeros
2.6. Exercises
3. A General Solution to the Output-Zeroing Problem
3.1. Preliminary Characterization of Invariant Zeros
3.2. Output-Zeroing Inputs
3.3. Exercises
4. The Moore-Penrose Pseudoinverse of the First Nonzero Markov
Parameter
4.1. Strictly Proper Systems
4.2. Proper Systems
4.3. Systems with Vector Relative Degree
4.4. Exercises
5. Singular Value Decomposition of the First Nonzero Markov
Parameter
5.1. Strictly Proper Systems
5.2. A Procedure for Computing Invariant Zeros of Strictly Proper
Systems
5.3. Proper Systems
5.4 A Procedure for Computing Invariant Zeros of Proper Systems
5.5. Exercises
6. Geometric Characterization of Zeros
6.1. Reachable/Observable System Structure
6.2. Systems with Zero Transfer-Function Matrix
6.3. The First Nonzero Markov Parameter of Full Column Rank
6.4. Invariant Subspaces
6.5. SVD and Output-Zeroing Problem
6.6. Proper Systems
6.7. Exercises
7. Singular Systems
7.1. Definitions of Zeros
7.2. Invariant Zeros
7.3. Output Decoupling Zeros
7.4. Input Decoupling Zeros
A. Appendix A
A.1. Controllability and Observability
A.2. Canonical Decomposition of the State Space
B. Appendix B
B.1. The Moore-Penrose Pseudoinverse of a Matrix
B.2. Singular Value Decomposition of a Matrix
B.3. Endomorphims of a Linear Space over C
C. Appendix C
C.1. Polynomial and Rational Matrices
References
Index
