Synthesis of Interval Observers for Nonlinear Discrete-Time Systems

TL;DR

This paper presents a systematic method for designing interval observers for nonlinear discrete-time systems using semidefinite programming, applicable with or without coordinate transformations, and validated through numerical examples.

Contribution

It introduces a novel systematic synthesis procedure for interval observers in nonlinear discrete-time systems, including conditions for coordinate transformations.

Findings

Effective interval observers designed for nonlinear discrete-time systems

Semidefinite feasibility programs used for gain computation

Numerical examples demonstrate practical applicability

Abstract

A systematic procedure to synthesize interval observers for nonlinear discrete-time systems is proposed. The feedback gains and other matrices are found from the solutions to semidefinite feasibility programs. Two cases are considered: (1) the interval observer is in the same coordinate frame as the given system, and (2) the interval observer uses a coordinate transformation. The conditions where coordinate transformations are necessary are detailed. Numerical examples are provided to showcase the effectiveness of the interval observers and demonstrate their application to sampled-data systems.