ATSI course on "Stabiliation of dynamical systems"
[lecture notes]

1. Notes on stability theory (definitions, basic thms)

2. Notes on feedback linearization (NB: PDF from the internet, based on Khalil's "Nonlinear systems")

3. Notes on Lyapunov-based control ---pages from the book:

  • M. Krstic, I. Kanellakopoulos, P. Kokotovic, "Nonlinear and Adaptive Control Design", John Wiley & Sons: NY, 1995


3. Notes on passivity theory (definitions, basic thms)

The course material on input-output stability essentially follows

The latter, in turn, is based on

  • M. Vidyasagar, "Nonlinear systems analysis", Prentice-Hall International, 1993.

For a more in-depth treatment of input-output stability see

  • C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press; 1st edition (March 21, 1975)

The following text presents a thorough treatment of passivity theory, specially for linear systems:

  • B. Brogliato, R. Lozano, B. Mashcke, and O. Egeland, "Dissipative systems analysis and control". Series Comunications and Control Engineering, Springer Verlag, London, 1st ed. 2000, 2nd ed. 2007.

4. Notes on passivity-based control

The passivity-based control method for nonlinear systems, which consists in controlling a system by rendering it passive, via feedback, was first introduced in

--see also the short note, which develops upon the latter,

  • R. Ortega, Passivity properties for stabilization of cascaded nonlinear systems, Automatica, Volume 27, Issue 2, March 1991, Pages 423-424

The idiom  "passivity-based control", however, was first employed in

  • R. Ortega, "Adaptive motion control of rigid robots: A tutorial", Automatica, Volume 25, Issue 6, November 1989, Pages 877-888

in the analysis, based on passivity theory, of a particular adaptive controller for robot manipulators.

The following paper was a milestone, due to its orignalility and generality, in the realm of passivity and internal stability analalysis, as well as in the context of passivity/based control:

Yet, passivity-based control of nonlinear systems has earlier precedent, as is in the so-called approach of energy shaping (to modify the potential energy/storage funciton) of robotic manipulators --see

For the purpose of this course, the following is a simple presentation of the essence of passivity-based control, with particular emphasis on Lagrangian systems:

Some more bibliography

General knowledge:

To succeed a good PhD thesis on automatic control it is strongly advised to revise, cover to cover: