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AuthorDelchamps, David F. author
TitleState Space and Input-Output Linear Systems [electronic resource] / by David F. Delchamps
ImprintNew York, NY : Springer New York, 1988
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Descript X, 425 p. online resource


It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year graduยญ ate level linear system theory course in the School of Electrical Engineering at Cornell. The members of the class have always come from a variety of departments and backgrounds, and conยญ sequently have entered the class with levels of preparation ranging from first year calculus and a taste of transform theory on the one extreme to senior level real analysis and abstract algebra on the other


I Mathematical Preliminaries -- 1. Some Linear Algebra -- 2. Linear Differential Equations: Existence and Uniqueness Theorems -- 3. Linear Difference Equations -- 4. Some More Linear Algebra -- 5. Dual Spaces, Norms, and Inner Products -- II State Space Linear Systems -- 6. State Space Linear Systems: Formal Definitions and General Properties -- 7. Realizations -- 8. Eigenvectors, Eigenvalues, and Normal Modes -- 9. The M + N Decomposition for Matrices Which are Not Semi-Simple -- 10. Complex Matrices and the Unitary Diagonalizability of Hermitian Matrices -- 11. The Jordan Canonical Form -- 12. Positive Definiteness, Matrix Factorization, and an Imperfect Analogy -- 13. Reachability and Controllability for Time-Invariant Continuous-Time Systems -- 14. Reachability and Controllability for Time-Invariant Discrete-Time Systems -- 15. Observability for Time-Invariant Continuous-Time Systems -- 16. Observability and Constructibility for Time-Invariant Discrete-Time Systems -- 17. The Canonical Structure Theorem -- III Input-Output Linear Systems -- 18. Formal Definitions and General Properties -- 19. Frequency Responses and Transfer Functions of Time Invariant Continuous-Time Systems -- 20. Frequency Responses and Transfer Functions of Time-Invariant Discrete-Time Systems -- 21. Realizations and McMillan Degree -- 22. Polynomial Matrices and Matrix Fraction Descriptions -- IV Stability and Feedback -- 23. Stability of State Space Linear Systems -- 24. Stability of Input-Output Linear Systems -- 25. Feedback, Observers, and Canonical Forms -- 26. The Discrete-Time Linear Quadratic Regulator Problem -- 27. The Continuous-Time Linear Quadratic Regulator Problem -- References

Mathematics System theory Electrical engineering Mathematics Systems Theory Control Electrical Engineering Communications Engineering Networks


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