Relative controllability of linear stationary completely integrable Pfaff systems

Abstract

We consider a process described by stationary completely integrable Pfaff systems linear in the input and the control as well as in the output and the state. We study the state controllability properties of the Pfaff system for the case in which an arbitrary initial state (a constant vector) and an arbitrary terminal state (either a constant vector, or an analytic vector function, or a constant vector and an analytic vector function) are given. The terminal states belong to a subspace of the state space of the system. The entire set of Pfaff systems splits into three classes, in each of which we obtain conditions for the controllability of Pfaff systems in the class of analytic controls. The conditions are stated in terms of the rank of some matrices formed from the given matrices of the Pfaff system and the matrix that specifies the subspace of terminal states.