# Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 2, page 179-184
- ISSN: 1641-876X

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topGurfil, Pini. "Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 179-184. <http://eudml.org/doc/207633>.

@article{Gurfil2003,

abstract = {The L^\{P\} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^\{P\} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.},

author = {Gurfil, Pini},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {time-varying Lur'e systems; functional analysis; L^\{P\}-stability},

language = {eng},

number = {2},

pages = {179-184},

title = {Quantitative L^\{P\} stability analysis of a class of linear time-varying feedback systems},

url = {http://eudml.org/doc/207633},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Gurfil, Pini

TI - Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 2

SP - 179

EP - 184

AB - The L^{P} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^{P} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.

LA - eng

KW - time-varying Lur'e systems; functional analysis; L^{P}-stability

UR - http://eudml.org/doc/207633

ER -

## References

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