Linearization by input–output injections on homogeneous time scales

Abstract

The problem of linearization by input-output (i/o) injections is addressed for nonlinear single-input single-output systems, defined on a homogeneous time scale. The paper provides conditions for the existence of a state transformation, bringing state equations into the observer form, which is linear up to some nonlinear input- and output-dependent functions, called i/o injections. These conditions are based on differential one-forms, associated with the i/o equation of the system.