Trajectory Funnels of Two-Dimensional Bilinear Control Systems

摘要

Two-dimensional linear nonstationary systems under the conditions of parametrical interval indeterminacy, when the only known about the coefficient matrix of these systems is that it satisfies some matrix range restriction, are considered. Qualitative methods of the investigation of two-dimensional dynamic systems, based on the concept of a phase portrait, are developed. Extreme matrix-valued functions determining the branches of the boundaries of trajectory funnels are synthesized by a differential geometric method. The geometric interpretation of the straight lines of switching is given. The properties of boundaries of trajectory funnels including the singular mode are investigated.