chapter  6
54 Pages


ByHebertt Sira-Ramirez, Marisol Delgado

Passive systems are characterized by the existence of a scalar energy storage function (“storage function” in short) such that its rate of change, along the controlled systems trajectories, is never superior to the supply rate represented by the product of the input and the output. In other words, the total stored energy in the system is inferior to the total energy delievered

A more general form of passivity is that of d i s s i p a t i v i t y , from where, historically speaking, all known results have developed. General studies about dissipativity and postivity were first provided by Willems in the context of abstract operators.22 The extension of these results to the case of nonlinear systems, which are affine in the control input, were given in the works by5,6. A geometric treatment of passive systems and feedback equivalence to passivity was given in the work o f3. Fundamental developments can also be found in the work o f 10 and also in the several articles by 12. Non trivial applications of passivity based control, ranging from robotics to synchronous motors and power electronics have been given by 16_18. The reader may explore a

complete and excellent exposition, with many historical references, in the recent book by 21. The topic of passivity has also been treated in many textbooks. An enlightening presentation is that of 8. The reader may also benefit from the treatment of the subject given in the textbook by 19.