Titlebook: Mathematical Control Theory; Deterministic Finite Eduardo D. Sontag Textbook 1998Latest edition Springer Science+Business Media New York 19

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Feedback and Stabilization,described in Chapter 1, as well as an elementary introduction to Lyapunov’s direct method and a proof of a “l(fā)inearization principle” for stability. Some more “advanced” topics on nonlinear stabilization are also included, mostly to indicate some of the directions of current research.

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Introduction,d devices that incorporate various mathematical techniques. These devices range from Watt’s steam engine governor, designed during the English Industrial Revolution, to the sophisticated microprocessor controllers found in consumer items —such as CD players and automobiles— or in industrial robots and airplane autopilots.

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Outputs,ortional-only (as opposed to proportional-derivative) control. Section 1.6, in particular, should be reviewed at this point, for a motivational introduction to observability, observers, and dynamic feedback, topics which will be developed next.

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Optimality: Multipliers, for arbitrary control-value sets but free final state. The area of nonlinear optimal control is very broad, and technically subtle, and, for a more in-depth study, the reader should consult the extensive literature that exists on the subject.

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