Necessary and sufficient conditions for transformation of nonholonomic system into time-state control form

Necessary and sufficient conditions for transformation of nonholonomic system into the time-state control form are given. Free flying space robot system is an example of the systems subject to nonholonomic constraints. Those systems modeled in state equation can not be stabilized with continuous static state feedback, thus we can not design stabilizing controllers for such systems using conventional methods. We have proposed time-state control form and its control strategy to control such nonholonomic systems, and the theorem given in this paper will show the effectiveness of our strategy.