Mapping of the linear systems of the second order with two-dimensional control
DOI:
https://doi.org/10.26565/2221-5646-2012-1018-01Keywords:
Linear control system, two-dimensional controlAbstract
This paper deals with linear control systems with two-dimensional control. The main goal of the paper is to find the exact analytic solution of the time-optimal control problem for an arbitrary linear control system with constant coefficients using the analytic solution of this problem for the simplest system. For this aim, we construct a certain nonsmooth mapping between the 0-controllability sets of the given systems. In other words, by means of this mapping, we investigate the equivalence of the systems with the same qualitative behavior in a neighborhood of the stationary point.
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