Towards backstepping design for incremental stability

The notion of incremental stability has been successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need for design methods for incremental stability. In this paper, we take a step in this direction by developing a backstepping design approach to incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a magnetic levitator incrementally stable.