Finite horizon robustness analysis of LTV systems using integral quadratic constraints

Peter Seiler; Robert M. Moore; Chris Meissen; Murat Arcak; Andrew Packard

doi:10.1016/j.automatica.2018.11.009

Finite horizon robustness analysis of LTV systems using integral quadratic constraints

Peter Seiler, Robert M. Moore, Chris Meissen, Murat Arcak, Andrew Packard

Aerospace Engineering and Mechanics

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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.

Original language	English (US)
Pages (from-to)	135-143
Number of pages	9
Journal	Automatica
Volume	100
DOIs	https://doi.org/10.1016/j.automatica.2018.11.009
State	Published - Feb 2019

Bibliographical note

Funding Information:
The material in this paper was not presented at any conference. The authors acknowledge funding from ONR, United States project N00014-18-1-2209. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton.

Publisher Copyright:
© 2018 Elsevier Ltd

Keywords

Integral quadratic constraints
Linear time varying
Robustness

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title = "Finite horizon robustness analysis of LTV systems using integral quadratic constraints",

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.",

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AU - Seiler, Peter

AU - Moore, Robert M.

AU - Meissen, Chris

AU - Arcak, Murat

AU - Packard, Andrew

N1 - Funding Information: The material in this paper was not presented at any conference. The authors acknowledge funding from ONR, United States project N00014-18-1-2209. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton. Publisher Copyright: © 2018 Elsevier Ltd

PY - 2019/2

Y1 - 2019/2

N2 - 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.

AB - 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.

KW - Integral quadratic constraints

KW - Linear time varying

KW - Robustness

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JO - Automatica

JF - Automatica

ER -

Finite horizon robustness analysis of LTV systems using integral quadratic constraints

Abstract

Bibliographical note

Keywords

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