### 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 | |

State | Published - Feb 1 2019 |

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### Keywords

- Integral quadratic constraints
- Linear time varying
- Robustness

### Cite this

*Automatica*,

*100*, 135-143. https://doi.org/10.1016/j.automatica.2018.11.009

**Finite horizon robustness analysis of LTV systems using integral quadratic constraints.** / Seiler Jr, Peter J; Moore, Robert M.; Meissen, Chris; Arcak, Murat; Packard, Andrew.

Research output: Contribution to journal › Article

*Automatica*, vol. 100, pp. 135-143. https://doi.org/10.1016/j.automatica.2018.11.009

}

TY - JOUR

T1 - Finite horizon robustness analysis of LTV systems using integral quadratic constraints

AU - Seiler Jr, Peter J

AU - Moore, Robert M.

AU - Meissen, Chris

AU - Arcak, Murat

AU - Packard, Andrew

PY - 2019/2/1

Y1 - 2019/2/1

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

UR - http://www.scopus.com/inward/record.url?scp=85057216739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057216739&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2018.11.009

DO - 10.1016/j.automatica.2018.11.009

M3 - Article

VL - 100

SP - 135

EP - 143

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -