Control of Time-Delay Systems Using Continuous-Time and Sampled-Data Models

摘要

The possibility of sampled-data feedback control for linear time-invariant multiple delay systems is studied using the constraint of piecewise constant time-control inputs. A split system representation is used to derive both necessary and sufficient conditions for control of the system state to the nullfunction in the state space. An algebraic condition necessary for controlling the state of linear time-invariant delay systems to the nullfunction is used to determine the concomitant structural properties of second and third order systems. It is shown that the characteristic quasipolynomials for the undriven systems are polynomials of second and third order, respectively. Notions of exponential stability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays. Methods for determining a stabilizing feedback are presented.