Finite horizon robustness analysis of LTV systems using integral quadratic constraints. (February 2019)

• Record Type: Journal Article
• Authors: Seiler, Peter; Moore, Robert M.; Meissen, Chris; Arcak, Murat; Packard, Andrew
• Is Part Of: Automatica. Volume 100(2019)
• Page Start: 135
• Page End: 143
• Publication Date: 2019-02
• Subjects: Robustness -- Integral quadratic constraints -- Linear time varying; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.11.009
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as an interconnection of a known LTV system and a perturbation. The input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Typical notions of robustness, e.g. nominal stability and gain/phase margins, can be insufficient for finite-horizon analysis. Instead, this paper focuses on robust induced gains and bounds on the reachable set of states. Sufficient conditions to compute robust performance bounds are formulated using dissipation inequalities and IQCs. The analysis conditions are provided in two equivalent forms as Riccati differential equations and differential linear matrix inequalities, and an algorithm is developed leveraging both forms.