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A Trajectory-Based Approach for the Stability Robustness of Nonlinear Systems with Inputs

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Abstract.

 We show, for two different definitions of semiglobal practical external stability, that the stability property holds on semi-infinite time intervals if and only if it holds on arbitrarily long but finite time intervals. These results have immediate applications in the analysis of the stability properties of highly oscillatory systems with inputs using averaging or for systems with inputs that are slowly varying. Results are stated for general flows and the stability is given with respect to arbitrary (not necessarily compact) sets.

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Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, University of Firenze, Via di Santa Marta 3, 50139 Firenze, Italy. angeli@dsi.unifi.it., , , , , , IT

    D. Angeli

  2. Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia. d.nesic@ee.mu.oz.au., , , , , , AU

    D. Nešić

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  1. D. Angeli
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  2. D. Nešić
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Additional information

Date received: May 11, 2001. Date revised: March 14, 2002.

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Angeli, D., Nešić, D. A Trajectory-Based Approach for the Stability Robustness of Nonlinear Systems with Inputs. Math. Control Signals Systems 15, 336–355 (2002). https://doi.org/10.1007/s004980200014

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  • DOI: https://doi.org/10.1007/s004980200014

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