An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Alexey Zhirabok; Alexey Shumsky

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 3, page 507-522
  • ISSN: 1641-876X

Abstract

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The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.

How to cite

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Alexey Zhirabok, and Alexey Shumsky. "An approach to the analysis of observability and controllability in nonlinear systems via linear methods." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 507-522. <http://eudml.org/doc/244049>.

@article{AlexeyZhirabok2012,
abstract = {The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.},
author = {Alexey Zhirabok, Alexey Shumsky},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear dynamic systems; observability; controllability; linear systems; decomposition; nonlinear systems},
language = {eng},
number = {3},
pages = {507-522},
title = {An approach to the analysis of observability and controllability in nonlinear systems via linear methods},
url = {http://eudml.org/doc/244049},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Alexey Zhirabok
AU - Alexey Shumsky
TI - An approach to the analysis of observability and controllability in nonlinear systems via linear methods
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 3
SP - 507
EP - 522
AB - The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.
LA - eng
KW - nonlinear dynamic systems; observability; controllability; linear systems; decomposition; nonlinear systems
UR - http://eudml.org/doc/244049
ER -

References

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