Abstract
This paper introduces a new technique for the analysis of time-optimal control of linear systems. A family of easily calculated invariants is developed and, for an important class of two-input systems, is shown to provide a complete description of the time-optimal flow near the origin. The two switching surfaces are described analytically and qualitatively in topological terms. The time-optimal feedback function is defined and analyzed with respect to its complexity and sensitivity to errors in state variable measurement. The results lead to the first explicit construction of a local regular synthesis for multi-input systems of arbitrary order.
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