Passivity-Based Analysis of Sampled and Quantized Control Implementations

TL;DR

This paper analyzes how sampling and quantization affect the passivity and stability of control systems, providing conditions to ensure boundedness and robustness of digital implementations.

Contribution

It introduces a passivity-based framework to evaluate sampled and quantized control implementations, including approximate bisimulation analysis, for the first time.

Findings

Passivity indices degrade under sampling and quantization.

Conditions are derived to guarantee state boundedness in digital control systems.

Approximate bisimulation can effectively model quantized control implementations.

Abstract

This paper studies the performance of a continuous controller when implemented on digital devices via sampling and quantization, by leveraging passivity analysis. Degradation of passivity indices from a continuous-time control system to its sampled, input and output quantized model is studied using a notion of quasi-passivity. Based on that, the passivity property of a feedback-connected system where the continuous controller is replaced by its sampled and quantized model is studied, and conditions that ensure the state boundedness of the interconnected system are provided. Additionally, the approximate bisimulation-based control implementation where the controller is replaced by its approximate bisimilar symbolic model whose states are also quantized is analyzed. Several examples are provided to illustrate the theoretical results.