Riassunto
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 gradu 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 con 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.
Contenuti
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.
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