ATSI course on Passivity-based control
[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 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:

A good way to deepen one's knowledge on passivity based control is in the context of Lagrangian systems, which include, e.g. robot manipulators, certain drones, electrical systems, autonomous vehicles, etc. The following text focusses on power converters, electrical motors and manipulators:

  • R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. Series Comunications and Control Engineering, Springer Verlag, London, 1998. ISBN 1-85233-016-3

but the controllers therein may serve as source of inspiration for more modern complex systems, such as networks of Lagrangian systems ... 

Some more bibliography

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

  • H. Khalil, "Nonlinear systems": 1st ed. McMillan 1992; 2nd and 3rd eds. Prentice Hall (1996 & 2002).