ABSTRACT
Given a (differentiable) signal, it is an important task for many applications to estimate on line its derivatives. Some well-known algorithms to solve this problem include the (continuous) high-gain observers and (discontinuous) Levant's exact differentiators. With exception of the linear high-gain observers, a systematic design of the gains of nonlinear differentiators is, in general, a difficult task and an open research field. In this work, we propose a novel method for the gain-tuning of a family of homogeneous differentiators which estimate the time-derivatives of a signal in finite-time. We show that the stability analysis and the gain-tuning of such differentiators can be done under a unified Lyapunov function framework, and it is converted to a sum of squares problem, that can be solved using LMIs, much in the same spirit of the linear systems.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. For definitions of strong and weak stability, see, for example, Filippov (Citation1988).
2. For a more detailed study of SOS forms, see, for example, Marshall (Citation2008)