摘要：AbstractIn contrast to the well-developed gain analysis for multi-input-multi-output (MIMO) linear time-invariant (LTI) systems, the research on the phase analysis does not share the same status. In this paper, we introduce the phase response of a class of discrete-time (DT) LTI multivariable system by exploiting a definition of matrix phases based on the numerical range. Half-sectorial transfer matrices are defined, which can generalize the positive real and negative imaginary systems. A sectored real lemma is obtained to characterize the phase information of a half-sectorial system from a state-space realization. Motivated by finding a phasic counterpart to the small gain theorem, we develop a small phase theorem for the internal stability of closed-loop systems.
关键词：Keywordsdiscrete-time LTI multivariable systemsphase responsesmall phase theoremsectored real lemma
