Adaptive stabilization of 3rd-order MIMO systems with uncertain control direction

This paper discusses the problem of stabilizing third order MIMO system whose constant high-frequency gain matrix contains elements of unknown signs. This scenario is commonly referred to as the control problem of systems with "uncertain control direction" and it has not been satisfactorily addressed yet in the MIMO setting. We develop a geometric framework to solve the underlying stabilization problem by a discontinuous feedback control inspired to the so-called "unit vector" method.