Geodesic
Singular sets and dynamic properties of bilinear control systems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 105-117

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The paper deals with qualitative methods of investigation of dynamic systems with control. Classification of singular sets of two-dimensional bilinear control systems is proposed. Constructive criteria of presence of different kinds of singular sets in the phase portrait are obtained. Dependence of dynamic properties of systems such as oscillation, stability, instability, and controllability on the types of singular sets is investigated. Analytical conditions under which analysis of above properties is relatively simple are obtained. 
@article{FPM_2005_11_8_a4,
     author = {V. N. Zhermolenko},
     title = {Singular sets and dynamic properties of bilinear control systems},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {105--117},
     publisher = {mathdoc},
     volume = {11},
     number = {8},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/}
}
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V. N. Zhermolenko. Singular sets and dynamic properties of bilinear control systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 105-117. http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/