On Convex Embedding and Control Design for Nonlinear Homogeneous Systems

Konstantin Zimenko (1) , Andrey Polyakov (2) , Denis Efimov (2)

1 ITMO University [Russia]
2 VALSE - Finite-time control and estimation for distributed systems

The paper presents methods for nonlinear homogeneous systems representation in a canonical form allowing stability conditions to be given by a linear matrix inequality. The main restriction for a system to admit the required representation is that its right-hand side has to be bounded on a unit sphere. It is shown that some nonhomogeneous systems can also be presented in the canonical form. Based on canonical representation a stabilizing control algorithm for affine in control nonlinear systems is presented with LMI-based tuning procedure. The results are supported with numerical examples.

Domaines: Automatique

Konstantin Zimenko, Andrey Polyakov, Denis Efimov. On Convex Embedding and Control Design for Nonlinear Homogeneous Systems. European Control Conference 2021, Jun 2021, Rotterdam, Netherlands. ⟨hal-03283069⟩