Linearization of discrete-time control system by state transformation

Abstract

This paper presents necessary and sufficient linearizability conditions by state transformation for discrete-time multi-input nonlinear control system under the mild assumption on the surjectivity property and describes how to find the state transformation when it exists. The conditions are formulated in terms of backward shifts of vector fields, defined by the system dynamics. The conditions are compared with those that allow additionally the regular static state feedback. The theory is illustrated by two examples.

Keywords

• nonlinear control system
• discrete-time system
• backward shifts of vector fields
• state linearizability.