LFT modelling and $\mu$-based robust performance analysis of hybrid multi-rate control systems

TL;DR

This paper develops an LFT-based method for analyzing the robust stability and $H_ Infty$ performance of hybrid multi-rate control systems with uncertainties, using a single-rate discrete-time model that captures discretization errors.

Contribution

It introduces a novel LFT modeling approach that simplifies the analysis of hybrid multi-rate systems with uncertainties, enabling guaranteed performance evaluation.

Findings

The LFT model accurately covers the hybrid system outputs at sampling times.

The method effectively assesses robust stability and $H_ Infty$ performance.

Validated on a multi-rate attitude control system example.

Abstract

This paper focuses on robust stability and $H_\infty$ performance analyses of hybrid continuous/discrete time linear multi-rate control systems in the presence of parametric uncertainties. These affect the continuous-time plant in a rational way which is then modeled as a Linear Fractional Transformation (LFT). Based on a zero-order-hold (ZOH) LFT discretization process at the cost of bounded quantifiable approximations, and then using LFT-preserving down-sampling operations, a single-rate discrete-time closed-loop LFT model is derived. Interestingly, for any step inputs, and any admissible values of the uncertain parameters, the outputs of this model cover those of the initial hybrid multi-rate closed-loop system at every sampling time of the slowest control loop. Such an LFT model, which also captures the discretization errors, can then be used to evaluate both robust stability and guaranteed $H_\infty$ performance with a $\mu$-based approach. The proposed methodology is illustrated on a realistic and easily reproducible example inspired by the validation of multi-rate attitude control systems.