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Singular sets and dynamic properties of bilinear control systems

Abstract

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 the presence of different kinds of singular sets in the phase portrait are obtained. The 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 the above properties is relatively simple are obtained.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 105–117, 2005.

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Zhermolenko, V.N. Singular sets and dynamic properties of bilinear control systems. J Math Sci 147, 6623–6630 (2007). https://doi.org/10.1007/s10958-007-0498-2

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Keywords

  • Phase Portrait
  • Invariant Manifold
  • Relative Equilibrium
  • Bilinear System
  • Boundary Vector