Less conservative robustness analysis of linear parameter varying systems using integral quadratic constraints

Pfifer, Harald; Seiler, Peter

Abstract

This paper considers the robustness of a feedback connection of a known linear parameter varying system and a perturbation. A sufficient condition is derived to bound the worst‐case gain and ensure robust asymptotic stability. The input/output behavior of the perturbation is described by multiple integral quadratic constraints (IQCs). The analysis condition is formulated as a dissipation inequality. The standard approach requires a non‐negative definite storage function and the use of ‘hard’ IQCs. The term ‘hard’ means that the IQCs can be specified as time‐domain integral constraints that hold over all finite horizons. The main result demonstrates that the dissipation inequality condition can be formulated requiring neither a non‐negative storage function nor hard IQCs. A key insight used to prove this result is that the multiple IQCs, when combined, contain hidden stored energy. This result can lead to less conservative robustness bounds. Two simple examples are presented to demonstrate this fact

Citation

Pfifer, H., & Seiler, P. (2016). Less conservative robustness analysis of linear parameter varying systems using integral quadratic constraints. International Journal of Robust and Nonlinear Control, 26(16), 3580-3594. https://doi.org/10.1002/rnc.3521

• Journal Article Type: Article
• Acceptance Date: Dec 22, 2015
• Online Publication Date: Feb 4, 2016
• Publication Date: Nov 10, 2016
• Deposit Date: Jun 4, 2018
• Print ISSN: 1049-8923
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 16
• Pages: 3580-3594
• DOI: https://doi.org/10.1002/rnc.3521
• Public URL: https://nottingham-repository.worktribe.com/output/1116029
• Publisher URL: https://onlinelibrary.wiley.com/doi/full/10.1002/rnc.3521