  In this paper, we define the phase response for a class of multi-input
multi-output (MIMO) linear time-invariant (LTI) systems whose frequency
responses are (semi-)sectorial at all frequencies. The newly defined phase
concept subsumes the well-known notions of positive real systems and negative
imaginary systems. We formulate a small phase theorem for feedback stability,
which complements the celebrated small gain theorem. The small phase theorem
lays the foundation of a phase theory of MIMO systems. We also discuss
time-domain interpretations of phase-bounded systems via both energy signal
analysis and power signal analysis. In addition, a sectored real lemma is
derived for the computation of MIMO phases, which serves as a natural
counterpart of the bounded real lemma.
