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

Zhirabok, A. ; Shumsky, A.

International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 3, pp. 507-522.

Résumé

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.

Détail

Keywords: nonlinear dynamic systems, observability, controllability, linear systems, decomposition
Mots-clés : system dynamiczny nieliniowy, obserwowalność, sterowalność, system liniowy, dekompozycja

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