  In this paper, we introduce a definition of phase response for a class of
multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the
frequency responses of which are cramped at all frequencies. This phase concept
generalizes the notions of positive realness and negative imaginariness. We
also define the half-cramped systems and provide a time-domain interpretation.
As a starting point in an endeavour to develop a comprehensive phase theory for
MIMO systems, we establish a small phase theorem for feedback stability, which
complements the well-known small gain theorem. In addition, we derive a
sectored real lemma for phase-bounded systems as a natural counterpart of the
bounded real lemma.
