Stability and control of linear systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer International Publishing
2019
Springer 2019 |
| Schriftenreihe: | Studies in systems, decision and control
185 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | XVII, 189 Seiten Illustrationen 23.5 cm x 15.5 cm |
| ISBN: | 9783030024048 3030024040 |
Internformat
MARC
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| 100 | 1 | |a Bacciotti, Andrea |d 1948- |e Verfasser |0 (DE-588)122673921 |4 aut | |
| 245 | 1 | 0 | |a Stability and control of linear systems |c Andrea Bacciotti |
| 264 | 1 | |a Cham |b Springer International Publishing |c 2019 | |
| 264 | 1 | |b Springer |c 2019 | |
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| 490 | 1 | |a Studies in systems, decision and control |v 185 | |
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| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 653 | |a Automatic Control | ||
| 653 | |a Canonical Decompositions | ||
| 653 | |a Control Theory | ||
| 653 | |a Controllability | ||
| 653 | |a Linear Control Systems | ||
| 653 | |a Linear Time Invariant Systems | ||
| 653 | |a Lyapunov Stability | ||
| 653 | |a Observability Matrix | ||
| 653 | |a Stability Theory | ||
| 653 | |a Static Output Feedback Stabilization | ||
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Datensatz im Suchindex
| _version_ | 1804179443682377728 |
|---|---|
| adam_text | Contents 1 Introduction.................................................................................................. 1.1 The Abstract Notion of System........................................................ 1.1.1 The Input-Output Operator.................................................... 1.1.2 Discrete Time and Continuous Time................................... 1.1.3 Input Space and Output Space............................................. 1.1.4 State Space............................................................................. 1.1.5 Finite Dimensional Systems................................................. 1.1.6 Connection of Systems........................................................... 1.1.7 System Analysis.................................................................... 1.1.8 Control System Design........................................................ 1.1.9 Properties of Systems............................................................. 1.2 Impulse Response Systems............................................................... 1.3 Initial Conditions................................................................................ 1.3.1 Deterministic Systems........................................................... 1.3.2 Time Invariant Systems........................................................ 1.3.3 Linear Systems...................................................................... 1.3.4 External Stability.................................................................... 1.3.5 Zero-Initialized Systems and Unforced Systems................ 1.4
Diiferential Systems........................................................................... 1.4.1 Admissible Inputs.................................................................. 1.4.2 State Equations...................................................................... 1.4.3 Linear Differential Systems.................................................... 1 1 1 3 3 3 4 4 5 6 7 8 12 13 14 14 15 15 16 16 16 18 2 Unforced Linear Systems........................................................................... 2.1 Prerequisites......................................................................................... 2.2 The Exponential Matrix.................................................................... 2.3 The Diagonal Case............................................................................. 2.4 The Nilpotent Case............................................................................. 2.5 The Block Diagonal Case.................................................................. 2.6 Linear Equivalence............................................................................. 21 21 23 25 25 27 28 xi
xii Contents 2.7 2.8 2.9 2.10 2.11 The Diagonalizable Case.................................................................... Jordan Form......................................................................................... Asymptotic Estimation of the Solutions.......................................... The Scalar Equation of Order n........................................................ The Companion Matrix...................................................................... 29 30 33 34 39 3 Stability of Unforced Linear Systems...................................................... 3.1 Equilibrium Positions......................................................................... 3.2 Conditions for Stability...................................................................... 3.3 Lyapunov Matrix Equation............................................................... 3.4 Routh-Hurwitz Criterion.................................................................... 43 43 44 46 50 4 Linear Systems with Forcing Term........................................................... 4.1 Nonhomogeneous Systems............................................................... 4.1.1 The Variation of Constants Method................................... 4.1.2 The Method of Undetermined Coefficients ........................ 4.2 Transient and Steady State............................................................... 4.3 The Nonhomogeneous Scalar Equation of Order n........................ 4.4 The Laplace Transform Method........................................................ 4.4.1 Transfer
Function.................................................................... 4.4.2 Frequency Response Analysis............................................... 53 53 54 55 57 59 62 62 66 5 Controllability and Observability of Linear Systems.......................... 5.1 The Reachable Sets............................................................................. 5.1.1 Structure of the Reachable Sets .......................................... 5.1.2 The Input-Output Map........................................................... 5.1.3 Solution of the ReachabilityProblem.................................. 5.1.4 The Controllability Matrix.................................................... 5.1.5 Hautus’ Criterion.................................................................... 5.2 Observability....................................................................................... 5.2.1 The Unobservability Space.................................................... 5.2.2 The Observability Matrix...................................................... 5.2.3 Reconstruction of the InitialState.......................................... 5.2.4 Duality..................................................................................... 5.3 Canonical Decompositions ............................................................... 5.3.1 Linear Equivalence............................................................... 5.3.2 Controlled Invariance............................................................. 5.3.3 Controllability
Form................................................................ 5.3.4 Observability Form............................................................... 5.3.5 Kalman Decomposition......................................................... 5.3.6 Some Examples...................................................................... 5.4 Constrained Controllability................................................................ 69 69 72 73 73 75 78 80 81 82 84 85 85 86 86 87 88 90 91 93
Contents xiii 6 External Stability......................................................................................... 6.1 Definitions........................................................................................... 6.2 Internal Stability.................................................................................. 6.3 The Case C = I.................................................................................. 6.4 The General Case................................................................................ 97 98 102 102 105 7 Stabilization................................................................................................... 7.1 Static State Feedback......................................................................... 7.1.1 Controllability......................................................................... 7.1.2 Stability.................................................................................. 7.1.3 Systems with Scalar Input.................................................... 7.1.4 Stabilizability........................................................................... 7.1.5 Asymptotic Controllability.................................................... 7.2 Static Output Feedback...................................................................... 7.2.1 Reduction of Dimension........................................................ 7.2.2 Systems with Stable Zero Dynamics................................... 7.2.3 A Generalized Matrix Equation .......................................... 7.2.4 A Necessary and
SufficientCondition.................................. 7.3 Dynamic Output Feedback............................................................... 7.3.1 Construction of an Asymptotic Observer............................ 7.3.2 Construction of the DynamicStabilizer................................ 7.4 РШ Control......................................................................................... Ill Ill 112 114 114 120 122 123 125 128 128 130 132 133 134 136 8 Frequency Domain Approach.................................................................... 8.1 The Transfer Matrix........................................................................... 8.2 Properties of the Transfer Matrix...................................................... 8.3 The Realization Problem.................................................................... 8.4 SISO Systems .................................................................................... 8.4.1 The Realization Problemfor SISO Systems......................... 8.4.2 External Stability.................................................................... 8.4.3 Nyquist Diagram.................................................................... 8.4.4 Stabilization by Static OutputFeedback.............................. 8.5 Disturbance Decoupling.................................................................... 139 139 142 144 148 148 151 155 157 159 Appendix A: Internal Stability Notions.......................................................... 165 Appendix B: Laplace
Transform..................................................................... 171 Index..................................................................................................................... 187
|
| any_adam_object | 1 |
| author | Bacciotti, Andrea 1948- |
| author_GND | (DE-588)122673921 |
| author_facet | Bacciotti, Andrea 1948- |
| author_role | aut |
| author_sort | Bacciotti, Andrea 1948- |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV045505089 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)1089442650 (DE-599)DNB1166586790 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:19:57Z |
| institution | BVB |
| institution_GND | (DE-588)1064344704 |
| isbn | 9783030024048 3030024040 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030889704 |
| oclc_num | 1089442650 |
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| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XVII, 189 Seiten Illustrationen 23.5 cm x 15.5 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
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| publisher | Springer International Publishing Springer |
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| series | Studies in systems, decision and control |
| series2 | Studies in systems, decision and control |
| spelling | Bacciotti, Andrea 1948- Verfasser (DE-588)122673921 aut Stability and control of linear systems Andrea Bacciotti Cham Springer International Publishing 2019 Springer 2019 XVII, 189 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Studies in systems, decision and control 185 Stabilität (DE-588)4056693-6 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Automatic Control Canonical Decompositions Control Theory Controllability Linear Control Systems Linear Time Invariant Systems Lyapunov Stability Observability Matrix Stability Theory Static Output Feedback Stabilization Lineares System (DE-588)4125617-7 s Stabilität (DE-588)4056693-6 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als Online-Ausgabe 9783030024055 Studies in systems, decision and control 185 (DE-604)BV041719311 185 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=cd16b45ae7334e28bcc2209a605403cc&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030889704&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bacciotti, Andrea 1948- Stability and control of linear systems Studies in systems, decision and control Stabilität (DE-588)4056693-6 gnd Lineares System (DE-588)4125617-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4125617-7 (DE-588)4032317-1 |
| title | Stability and control of linear systems |
| title_auth | Stability and control of linear systems |
| title_exact_search | Stability and control of linear systems |
| title_full | Stability and control of linear systems Andrea Bacciotti |
| title_fullStr | Stability and control of linear systems Andrea Bacciotti |
| title_full_unstemmed | Stability and control of linear systems Andrea Bacciotti |
| title_short | Stability and control of linear systems |
| title_sort | stability and control of linear systems |
| topic | Stabilität (DE-588)4056693-6 gnd Lineares System (DE-588)4125617-7 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Stabilität Lineares System Kontrolltheorie |
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| volume_link | (DE-604)BV041719311 |
| work_keys_str_mv | AT bacciottiandrea stabilityandcontroloflinearsystems AT springerinternationalpublishing stabilityandcontroloflinearsystems |