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Convergence Rate of Nonlinear Switched Systems

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Philippe Jouan (LMRS), Saïd Naciri (LMRS)

Optimization and Control · Submitted 5 Nov 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time.

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arXiv ID1511.01737 (version 1)
Pith IDSO2S3UQA, Pith's permanent record of this paper and its review
CitationPhilippe Jouan (LMRS), Sa\"id Naciri (LMRS). "Convergence Rate of Nonlinear Switched Systems." arXiv:1511.01737 (2015). https://pith.science/paper/SO2S3UQA
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,101 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.65 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.30 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. background 0.81 0.33 0.04 asserted 0.74
s1 We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. contribution 0.65 0.23 0.04 asserted 0.99
s2 We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. result 1.00 0.92 0.26 asserted 1.00
s3 Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. contribution 0.72 0.31 0.04 asserted 0.81
s4 Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time. result 0.81 0.95 0.36 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time.

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