Bittanti / Colaneri Periodic Systems

Filtering and Control
1. Auflage 2008
ISBN: 978-1-84800-911-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 424 Seiten

gives a comprehensive treatment of the theory of periodic systems, including the problems of filtering and control. Topics covered include: basic issues, including Floquet theory, controllability and observability, canonical decomposition, system norms and Lyapunov and robust stability; the problem of state estimation in its various forms, filtering, prediction and smoothing; control design methods, particularly optimal and robust control. The text focuses on discrete-time signals and systems; however, an overview of the entire field, including the continuous-time case, is provided in the first chapter. The authors’ presentation of the theory and results is mathematically rigorous while maintaining a readable style, avoiding excessive formalism. This makes the book accessible to graduate students and researchers from the fields of engineering, physics, economics and mathematics.

Autoren/Hrsg.

Bittanti, Sergio

Colaneri, Patrizio

Inhaltsverzeichnis

1;Communications and Control Engineering;2
2;Authors’ Note;7
3;Preface;9
4;Contents;15
5;Introduction;20
5.1;1.1 Periodic Models;20
5.2;1.2 Floquet–Lyapunov Theory;27
5.3;1.3 Lagrange Formula and External Stability;36
5.4;1.4 Relative Degrees and Zeros;38
5.5;1.5 Periodic Systems in Frequency Domain;45
5.6;1.6 Time-invariant Representations;49
5.7;1.7 Periodic Control of Time-invariant Systems;51
5.8;1.8 Periodic Control of Periodic Systems;66
5.9;1.9 Stochastic Periodic Signals;76
6;Linear Periodic Systems;79
6.1;2.1 The Periodic Transfer Operator;79
6.2;2.2 PARMA Model;83
6.3;2.3 The Transfer Operator in Frequency Domain;87
6.4;2.4 State–Space Description;91
6.5;2.5 Adjoint Operator and Its State–Space Description;97
6.6;2.6 Bibliographical Notes;98
7;Floquet Theory and Stability;99
7.1;3.1 Monodromy Matrix;99
7.2;3.2 Floquet Theory;104
7.3;3.3 Stability;108
7.4;3.4 Companion Forms;123
7.5;3.5 Bibliographical Notes;126
8;Structural Properties;127
8.1;4.1 Reachability and Controllability;127
8.2;4.2 Observability and Reconstructability;144
8.3;4.3 Canonical Decomposition;154
8.4;4.4 Extended Structural Properties;157
8.5;4.5 The Periodic Lyapunov Equation;160
8.6;4.6 Bibliographical Notes;172
9;Periodic Transfer Function and BIBO Stability;173
9.1;5.1 Elementary Algebra of Periodic Polynomials;173
9.2;5.2 Lifted Periodic Polynomials and Zeroes;175
9.3;5.3 Weak and Strong Coprimeness;180
9.4;5.4 Rational Periodic Operators;182
9.5;5.5 BIBO Stability and Finite Impulse Response;186
9.6;5.6 Bibliographical Notes;188
10;Time-invariant Reformulations;189
10.1;6.1 Sampling in the z-Domain;190
10.2;6.2 Time-lifted Reformulation;191
10.3;6.3 Cyclic Reformulation;198
10.4;6.4 The Frequency-lifted Reformulation;205
10.5;6.5 Bibliographical Notes;210
11;State–Space Realization;211
11.1;7.1 Periodic Realization from Lifted Models;213
11.2;7.2 Realization from a Fractional Representation;223
11.3;7.3 Balanced Realization;228
11.4;7.4 Bibliographical Notes;230
12;Zeros, Poles, and the Delay Structure;232
12.1;8.1 Cyclic Poles and Zeros;232
12.2;8.2 Lifted Poles and Zeros;235
12.3;8.3 Zeros via a Geometric Approach;240
12.4;8.4 Delay Structure and Interactor Matrix;245
12.5;8.5 Bibliographical Notes;251
13;Norms of Periodic Systems;252
13.1;9.1 L2 Norm;252
13.2;9.2 L8 Norm;261
13.3;9.3 Entropy;272
13.4;9.4 Hankel Norm and Order Reduction;275
13.5;9.5 Time-domain Specifications;278
13.6;9.6 Bibliographical Note;281
14;Factorization and Parametrization;282
14.1;10.1 Periodic Symplectic Pencil;282
14.2;10.2 Spectral Factorization;286
14.3;10.3 J-Spectral Factorization;293
14.4;10.4 Parametrization of Stabilizing Controllers;295
14.5;10.5 Bibliographical Notes;306
15;Stochastic Periodic Systems;307
15.1;11.1 Cyclostationary Processes;308
15.2;11.2 Spectral Representation;311
15.3;11.3 Spectrum from the Transfer Operator;312
15.4;11.4 Periodic State–Space Stochastic Models;317
15.5;11.5 Stochastic Realization;320
15.6;11.6 Bibliographical Notes;326
16;Filtering and Deconvolution;327
16.1;12.1 Filtering and Deconvolution in the H2 Setting;329
16.2;12.2 H2 Prediction;340
16.3;12.3 H2 Smoothing;345
16.4;12.4 Filtering and Deconvolution in the H8 Setting;350
16.5;12.5 H8 1-step Prediction;358
16.6;12.6 H8 Smoothing;361
16.7;12.7 Bibliographical Notes;368
17;Stabilization and Control;369
17.1;13.1 The Class of State-feedback Stabilizing Controllers;369
17.2;13.2 Robust Stabilization;371
17.3;13.3 Pole Assignment for Control;374
17.4;13.4 Exact Model Matching;378
17.5;13.5 H2 Full-information Optimal Control;384
17.6;13.6 State-feedback H8 Control;388
17.7;13.7 Static Output-feedback;391
17.8;13.8 Dynamic Output-feedback;398
17.9;13.9 Bibliographical Notes;421
18;References;422
19;Index;435