Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866913969939152896 |
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| author | Seiler, Peter Moore, Robert Meissen, Chris Arcak, Murat Packard, Andrew |
| author_facet | Seiler, Peter Moore, Robert Meissen, Chris Arcak, Murat Packard, Andrew |
| contents | 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 a connection 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. A computational approach is provided that leverages both forms of the analysis conditions. The approach is demonstrated with two examples |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_07248 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints Seiler, Peter Moore, Robert Meissen, Chris Arcak, Murat Packard, Andrew Systems and Control Optimization and Control 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 a connection 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. A computational approach is provided that leverages both forms of the analysis conditions. The approach is demonstrated with two examples |
| title | Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/1711.07248 |