Passivity-Based Control

Passivity is a fundamental property of many physical systems which may be roughly defined in terms of energy dissipation and transformation. It is an inherent Input-Ouput property in the sense that it quantifies and qualifies the energy balance of a system when stimulated by external inputs to generate some output. Passivity is therefore related to the property of stability in an input-output sense, that is, we say that the system is stable if bounded ``input energy'' supplied to the system, yields bounded output energy. This is in contrast to Lyapunov stability which concerns the internal stability of a system, that is, how ``far'' the state of a system is from a desired value. In other words, how differently a system behaves with respect to a desired performance. Passivity based control is a methodology which consists in controlling a system with the aim at making the closed loop system, passive. The field constitutes an active research direction and therefore in this article we give only a basic overlook of the most important concepts involved. A section is also devoted to a wide class of physical passive systems: the Euler-Lagrange (EL) systems and their passivity-based control. We do not claim any originality on the contents of this article. The reader should rather consider it as very concise image of the material cited in the Bibliography. Therefore, we invite the reader who wishes to obtain a deeper knowledge in the subject, to see those references.