Gain-Scheduling Controller Synthesis for Nested Systems with Full Block Scalings

TL;DR

This paper introduces a convex LMI-based framework for synthesizing structured gain-scheduled controllers for nested systems with time-varying parameters, enabling multi-objective control design.

Contribution

It develops a novel lifting technique for structured gain-scheduling synthesis applicable to nested systems with full block scalings, using convex LMIs.

Findings

Framework effectively handles multiple performance objectives.

Lifting technique simplifies structured gain-scheduling design.

Applicable to systems with nested inner and outer loops.

Abstract

This work presents a framework to synthesize structured gain-scheduled controllers for structured plants whose dynamics change according to time-varying scheduling parameters. Both the system and the controller are assumed to admit descriptions in terms of a linear time-invariant system in feedback with so-called scheduling blocks, which collect all scheduling parameters into a static system. We show that such linear fractional representations permit to exploit a so-called lifting technique in order to handle several structured gain-scheduling design problems. These could arise from a nested inner and outer loop control configuration with partial or full dependence on the scheduling variables. Our design conditions are formulated in terms of convex linear matrix inequalities and permit to handle multiple performance objectives.