Transformation of nonlinear discrete-time system into the extended observer form

ABSTRACT

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input–output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.

KEYWORDS:

• Discrete-time system
• nonlinear control system
• extended coordinate transformation
• output transformation
• extended observer form

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The assumption that the functions are meromorphic is necessary for the construction of the algebraic framework in Section 2.1.

2. The details about the properties of the extended coordinate transformation can be found in Huijberts (1999) for the case of autonomous systems.

3. The extended observer form without inputs was considered earlier in Huijberts (1999).

Additional information

Funding

This work was supported by the Estonian Research Competency Council, personal research funding [Grant Number PUT481].