Geometrical aspects of admissible regions in fixed-time pulse-frequency-modulated control systems

In previous optimization studies of pulse-frequency-modulated (PFM) control systems it is assumed that a control function exists which carries the system state to the desired final state. In this study a systematic method of determining the regions of initial states (admissible regions) from which the system state can be carried to the origin within a prespecified fixed time
T
is developed. The method presented makes use of the topological properties of the "pulse firing time,"β-space. Conditions for unique control are presented.