Backstepping to passivity: recursive design of adaptive systems

A major obstacle to the wider use of the passivity concept has been its limitation to systems of relative degree one. The relative degree limitation has been effectively removed by various forms of a recursive procedure called backstepping. It is shown how backstepping is used to design a generation of adaptive controllers for nonlinear systems. The backstepping procedure provides a framework for recursive designs by achieving, at each step, the strict passivity of a virtual system. In addition to boundedness, the systems designed by this procedure also possess strong convergence properties.