REFERENCES

1. J. W. Nillson, Electric Circuits, 2nd ed. Addison-Wesley, Reading, MA, 1986.
2. R. K. Livesley, Mathematical Methods for Engineering. Wiley, New York, 1989.
3. E. Kamen, Introduction to Signals and Systems. Macmillan, New York, 1987.
4. B. C. Kuo, Linear Circuits and Systems. McGraw-Hill, New York, 1987.
5. M. F. O’Flynn and G. Moriarti, Linear Systems. Harper and Row, New York, 1987.
6. MATLAB for MS-DOS Personal Computers, User’s Guide; The Control System Toolbox; The MathWorks, Inc., 1997.
7. S. J. Mason, “Feedback theory: Some properties of signal flow graphs.” Proc. IRE 41, 1144 (1953).
8. S. J. Mason, “Feedback theory: Further properties of signal flow graphs.” Proc. IRE 44, 920 (1956).
9. S. M. Shinners, A Guide to Systems Engineering and Management, Lexington Books, Lexington, MA, 1976.
10. S. Barnet, “Matrices, polynomials, and linear time-invariant systems.” IEEE Trans. Autom. Control AC-18, 1–10 (1973).
11. C. A. Desoer, “An introduction to state space techniques in linear systems.” In Proceedings of the 1962 Joint Automatic Control Conference, New York, pp. 10-2-1–10-2-5.
12. L.A. Zadeh, “An introduction to state-space techniques.” In Proceedings of the 1962 Joint Automatic Control Conference, New York, pp. 10-1-l–10-1-5.
13. D. F. Delchamps, State Space and Input-Output Linear Systems. Springer-Verlag, New York, 1988.
14. R. C. Rosenberg and D. C. Karnopp, Introduction to Physical System Design. McGraw-Hill, New York, 1987.
15. G. A. Korn and T. M. Korn, Electronic Analog and Hybrid Computers. McGraw-Hill, New York, 1964.
16. R. W. Hamming, Numerical Methods for Scientists and Engineers. McGraw-Hill, New York, 1962.
17. D. D. McCracken and W. S. Dorn, Numerical Methods and FORTRAN Programming. Wiley, New York, 1964.
18. K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed. Wiley, New York, 1989.
19. T. Ward and E. Bromhead, FORTRAN and the Art of PC Programming. Wiley, New York, 1989.
20. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra. Freeman, San Francisco, CA, 1963.
21. B. S. Morgan, Jr., “Sensitivity analysis and synthesis of multivariable systems.” IEEE Trans. Automat. Control AC-11, 506–512 (1966).
22. M. I. Liou, ”A novel method of evaluating transient response.” Proc. IEEE 54, 20–23 (1966).
23. B. O. Watkins, Introduction to Control Systems, pp. 258–259. Macmillan, New York, 1969.
24. J. S. Meditch, “On the problem of optimal thrust programming for a lunar soft landing.” IEEE Trans. Autom. Control, AC-9, 477–484 (1964).
25. F. J. Ellert and C. W. Merriam, III, “Synthesis of feedback controls using optimization theory—An example.” In Proceedings of the 1962 Joint Automatic Control Conference, New York, p. 19-1.
26. N. W. Rees, “An application of optimal control theory to the guided torpedo problem.” In Proceedings of the 1968 Joint Automatic Control Conference, pp. 820–825.
27. W. R. Emanuel and R. J. Mulholland, “Energy based dynamic model for Lago Pond, Georgia.” In Proceedings of the 1974 Joint Automatic Control Conference, pp. 354–362.
28. R. C. Dorf, Modern Control Systems, 7th ed. Addison-Wesley, Reading, MA, 1995.
29. D. Rockefeller, “The population problem and economic progress.” Vital Speeches 32, 366–370 (1966).
30. G. D’Ans, P. W. Kotovic, and D. Gottlieb, “A nonlinear regulator problem for a model of biological water treatment.” IEEE Trans. Autom. Control AC-16, 341–347 (1971).
31. The Student Edition of MATLAB, The Math Works, Inc., Prentice Hall, Englewood Cliffs, NJ, 1997.

*It is suggested that those readers who are unfamiliar with MATLAB read Sections A through E before writing MATLAB programs.

*All references to pages or manuals herein is for The Student Edition, unless otherwise annotated.

*The terms post- or premultiplication are used to indicate whether the matrix is multiplied from the right or the left, respectively.

*This analog computer simulation diagram contains more inverters than are actually required to implement Eqs. (2.225) and (2.226). It has been presented in this manner to indicate the proper phase relationships existing among the various states, as indicated in Eq. (2.227). From now on, all state-variable diagrams will also contain a sufficient number of inverters to indicate the proper phase relationships among the various states. It is left as an exercise to show how an analog computer simulation of Eqs. (2.225) and (2.226) can be performed using the same number of integrators and summers as shown in Figure 2.30, but with only one inverter.