Local Theory of Linear Systems with Noncommensurate Time Delays

摘要

Stability and feedback control of linear neutral (and retarded) time-delay systems with one or more noncommensurate time delays is studied. The Theory is based on a pointwise or local approach involving polynomial and rational functions in the complex variables s, z1, z2, ..., zq, with s evaluated at points in the right-half plane and the zi evaluated at points in the unit disc. In terms of this framework, an algebraic notion of stability, called pointwise stability, is defined and studied. Necessary and sufficient conditions are then given for the existence of a stabilizing dynamic output feedback compensator. The problem of stabilization using nondynamic state feedback is also briefly considered in the case when the system's input matrix has constant rank.