Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems

TL;DR

This paper develops convex LMI-based methods for robust and gain-scheduling ${ m H}_2$ control of uncertain LFT systems, enhancing disturbance rejection and robustness over traditional approaches.

Contribution

It introduces a novel convex synthesis framework using an intermediate matrix variable for robust and gain-scheduled ${ m H}_2$ control of parameter-dependent systems.

Findings

Controllers show reduced conservatism compared to ${ m H}_ ext{infty}$ designs.

Framework preserves classical ${ m H}_2$ interpretation and guarantees robustness.

Numerical examples validate improved disturbance rejection.

Abstract

This paper addresses the robust ${\cal H}_2$ synthesis problem for linear fractional transformation (LFT) systems subject to structured uncertainty (parameter) and white-noise disturbances. By introducing an intermediate matrix variable, we derive convex synthesis conditions in terms of linear matrix inequalities (LMIs) that enable both robust and gain-scheduled controller design for parameter-dependent systems. The proposed framework preserves the classical white-noise and impulse-response interpretation of the ${\cal H}_2$ criterion while providing certified robustness guarantees, thereby extending optimal ${\cal H}_2$ control beyond the linear time-invariant setting. Numerical and application examples demonstrate that the resulting robust ${\cal H}_2$ controllers achieve significantly reduced conservatism and improved disturbance rejection compared with conventional robust ${\cal H}_\infty$-based designs.