Total stability and integral action for discrete-time nonlinear systems

TL;DR

This paper extends the concept of total stability and integral action from continuous-time to discrete-time nonlinear systems, providing new tools for robustness analysis in digital control.

Contribution

It introduces a discrete-time framework for total stability and integral action, bridging a gap in robustness theory for nonlinear systems under digital control.

Findings

Discrete-time total stability results are established.

Robustness properties can be analyzed via model differences.

Equilibrium transfer under model similarity is characterized.

Abstract

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability is well established in the continuous-time nonlinear framework, the same cannot be stated for its discrete-time counterpart. In this paper, we propose the discrete-time parallel of total stability results for continuous-time nonlinear system. This enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on the