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AuthorWonham, W. Murray. author
TitleLinear Multivariable Control: a Geometric Approach [electronic resource] / by W. Murray Wonham
ImprintNew York, NY : Springer US, 1979
Edition Second Edition
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0068-7
Descript online resource

SUMMARY

In writing this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathematiยญ cians with some previous acquaintance with control problems. The present edition of this book is a revision of the preliminary version, published in 1974 as a Springer-Verlag "Lecture Notes" volume; and some of the remarks to follow are repeated from the original preface. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondly and of greater interest, the geometric setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and econoยญ mical; they are also easily reduced to matrix arithmetic as soon as you want to compute


CONTENT

0 Mathematical Preliminaries -- 0.1 Notation -- 0.2 Linear Spaces -- 0.3 Subspaces -- 0.4 Maps and Matrices -- 0.5 Factor Spaces -- 0.6 Commutative Diagrams -- 0.7 Invariant Subspaces. Induced Maps -- 0.8 Characteristic Polynomial. Spectrum -- 0.9 Polynomial Rings -- 0.10 Rational Canonical Structure -- 0.11 Jordan Decomposition -- 0.12 Dual Spaces -- 0.13 Tensor Product. The Sylvester Map -- 0.14 Inner Product Spaces -- 0.15 Hermitian and Symmetric Maps -- 0.16 Well-Posedness and Genericity -- 0.17 Linear Systems -- 0.18 Transfer Matrices. Signal Flow Graphs -- 0.19 Rouchรฉโ{128}{153}s Theorem -- 0.20 Exercises -- 0.21 Notes and References -- 1 Introduction to Controllability -- 1.1 Reachability -- 1.2 Controllability -- 1.3 Single-Input Systems -- 1.4 Multi-Input Systems -- 1.5 Controllability is Generic -- 1.6 Exercises -- 1.7 Notes and References -- 2 Controllability, Feedback and Pole Assignment -- 2.1 Controllability and Feedback -- 2.2 Pole Assignment -- 2.3 Incomplete Controllability and Pole Shifting -- 2.4 Stabilizability -- 2.5 Exercises -- 2.6 Notes and References -- 3 Observability and Dynamic Observers -- 3.1 Observability -- 3.2 Unobservable Subspace -- 3.3 Full Order Dynamic Observer -- 3.4 Minimal Order Dynamic Observer -- 3.5 Observers and Pole Shifting -- 3.6 Detectability -- 3.7 Detectors and Pole Shifting -- 3.8 Pole Shifting by Dynamic Compensation -- 3.9 Observer for a Single Linear Functional -- 3.10 Preservation of Observability and Detectability -- 3.11 Exercises -- 3.12 Notes and References -- 4 Disturbance Decoupling and Output Stabilization -- 4.1 Disturbance Decoupling Problem (DDP) -- 4.2 (A, B)-Invariant Subspaces -- 4.3 Solution of DDP -- 4.4 Output Stabilization Problem (OSP) -- 4.5 Exercises -- 4.6 Notes and References -- 5 Controllability Subspaces -- 5.1 Controllability Subspaces -- 5.2 Spectral Assignability -- 5.3 Controllability Subspace Algorithm -- 5.4 Supremal Controllability Subspace -- 5.5 Transmission Zeros -- 5.6 Disturbance Decoupling with Stability -- 5.7 Controllability Indices -- 5.8 Exercises -- 5.9 Notes and References -- 6 Tracking and Regulation I: Output Regulation -- 6.1 Restricted Regulator Problem (RRP) -- 6.2 Solvability of RRP -- 6.3 Extended Regulator Problem (ERP) -- 6.4 Example -- 6.5 Concluding Remarks -- 6.6 Exercises -- 6.7 Notes and References -- 7 Tracking and Regulation II: Output Regulation with Internal Stability -- 7.1 Solvability of RPIS: General Considerations -- 7.2 Constructive Solution of RPIS:


Mathematics System theory Calculus of variations Mathematics Systems Theory Control Calculus of Variations and Optimal Control; Optimization



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