New look at robust backstepping through state-dependent scaling design

This paper considers global and semi-global robust stabilization problems for a class of uncertain nonlinear systems and develops a new systematic tool for robust backstepping. By choosing state-dependent scaling functions in each step of the backstepping design, one can construct robust control laws for an extended class of strict feedback systems. The scaling approach to robust backstepping treats both static and dynamic uncertainty in a unified way. The method is amenable to automatic computation based on optimization, and one can thus introduce performance objectives such as instantaneous control effort minimization into the design.