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＜電子ブック＞
The Stability and Control of Discrete Processes / by J.P. LaSalle
(Applied Mathematical Sciences. ISSN:2196968X ; 62)

版	1st ed. 1986.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1986
本文言語	英語
大きさ	VIII, 150 p : online resource
冊子体	The stability and control of discrete processes / J.P. LaSalle ; : U.S,: Germany
著者標目	*LaSalle, J.P author SpringerLink (Online service)
件　名	LCSH:Probabilities FREE:Probability Theory
一般注記	1. Introduction -- 2. Liapunov’s direct method -- 3. Linear systems x’ = Ax. -- 4. An algorithm for computing An. -- 5. A characterization of stable matrices. Computational criteria. -- 6. Liapunov’s characterization of stable matrices. A Liapunov function for x’ = Ax. -- 7. Stability by the linear approximation. -- 8. The general solution of x’ = Ax. The Jordan Canonical Form. -- 9. Higher order equations. The general solution of ?(z)y = 0. -- 10. Companion matrices. The equivalence of x’ = Ax and ?(z)y = 0. -- 11. Another algorithm for computing An. -- 12. Nonhomogeneous linear systems x’ = Ax + f(n). Variation of parameters and undetermined coefficients. -- 13. Forced oscillations. -- 14. Systems of higher order equations P(z)y = 0. The equivalence of polynomial matrices. -- 15. The control of linear systems. Controllability. -- 16. Stabilization by linear feedback. Pole assignment. -- 17. Minimum energy control. Minimal time-energy feedback control. -- 18. Observability. Observers. State estimation. Stabilization by dynamic feedback. -- References Professor J. P. LaSalle died on July 7, 1983 at the age of 67. The present book is being published posthumously with the careful assistance of Kenneth Meyer, one of the students of Professor LaSalle. It is appropriate that the last publi­ cation of Professor LaSalle should be on a subject which con­ tains many interesting ideas, is very useful in applications and can be understood at an undergraduate level. In addition to making many significant contributions at the research level to differential equations and control theory, he was an excel­ lent teacher and had the ability to make sophisticated con­ cepts appear to be very elementary. Two examples of this are his books with N. Hasser and J. Sullivan on analysis published by Ginn and Co. , 1949 and 1964, and the book with S. Lefschetz on stability by Liapunov's second method published by Academic Press, 1961. Thus, it is very fitting that the present volume could be completed. Jack K. Hale Kenneth R. Meyer TABLE OF CONTENTS page 1. Introduction 1 2. Liapunov's direct method 7 3. Linear systems Xl = Ax. 13 4. An algorithm for computing An. 19 5. Acharacterization of stable matrices. Computational criteria. 24 6. Liapunovls characterization of stable matrices. A Liapunov function for Xl = Ax. 32 7. Stability by the linear approximation. 38 8. The general solution of Xl = Ax. The Jordan Canonical Form. 40 9. Higher order equations. The general solution of ~(z)y = O Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-1076-4

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