Singular Perturbation Theory for Piecewise-Linear Systems With Random Inputs

B. S. Heck; A. H. Haddad

doi:10.1080/07362998908809182

Singular Perturbation Theory for Piecewise-Linear Systems With Random Inputs

B. S. Heck, A. H. Haddad

Electrical and Computer Engineering

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

Abstract

The effect of random inputs on a continuous piecewise-linear singularly perturbed system is investigated in this paper. Reduced-order models are developed for a second-order system (one fast and one slow variable) which has a random input. It is shown that the solutions of the reduced-order models approximate the actual solutism with differences in probability density functions of order 0(m 5) (in a distributional sense). For the special case of a system which is linear in the fast variable, it is shown that the mean-squared error between the approximate and actual solutions in the fast time scale is of order 0(m). An outline is provided for the extehsion of the results to the vector variable case.

Original language	English (US)
Pages (from-to)	273-289
Number of pages	17
Journal	Stochastic Analysis and Applications
Volume	7
Issue number	3
DOIs	https://doi.org/10.1080/07362998908809182
State	Published - Jan 1989

Funding

ACKNOWLEDGEMENT This research was completed while both authors were at the Georgia Institute of Technology. The research was supported, in part, by the U.S. Air Force under Grant AFOSR-87-0308.

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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Cite this

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abstract = "The effect of random inputs on a continuous piecewise-linear singularly perturbed system is investigated in this paper. Reduced-order models are developed for a second-order system (one fast and one slow variable) which has a random input. It is shown that the solutions of the reduced-order models approximate the actual solutism with differences in probability density functions of order 0(m 5) (in a distributional sense). For the special case of a system which is linear in the fast variable, it is shown that the mean-squared error between the approximate and actual solutions in the fast time scale is of order 0(m). An outline is provided for the extehsion of the results to the vector variable case.",

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AB - The effect of random inputs on a continuous piecewise-linear singularly perturbed system is investigated in this paper. Reduced-order models are developed for a second-order system (one fast and one slow variable) which has a random input. It is shown that the solutions of the reduced-order models approximate the actual solutism with differences in probability density functions of order 0(m 5) (in a distributional sense). For the special case of a system which is linear in the fast variable, it is shown that the mean-squared error between the approximate and actual solutions in the fast time scale is of order 0(m). An outline is provided for the extehsion of the results to the vector variable case.

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Singular Perturbation Theory for Piecewise-Linear Systems With Random Inputs

Abstract

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