On the state-space analysis in the synthesis of time-optimal control for a class of linear systems

The paper deals with a new approach for synthesis of time-optimal control for a class of linear systems. It is based on the decomposition of the time-optimal control problem into a class of decreasing order problems, and the properties and relations between problems within this class. First, the problems state-spaces properties are analyzed, and then the optimal control is obtained by using a multi-stage procedure avoiding the switching hyper surface description. The emphasis in this paper is on the state-space analysis stage of the approach proposed.