Criteria for minimization of spectral abscissa of time-delay systems

Abstract

Spectral abscissa (SA) is defined as the real part of the rightmost characteristic root(s) of a dynamical system, and it can be regarded as the decaying rate of the system, the smaller the better from the viewpoint of fast stabilization. Based on the Puiseux series expansion of complex-valued functions, this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3. Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not, and they can be tested directly and easily.

The PDP feedback control design and exponential stability for a star-shaped network of open channels

“…It is found that the control design without considering the delay effect might be not reliable and not safe in applications, where the stability or control performance depends sharply on the delay changes, and then the delay effect on the system dynamics and control performance must be carefully studied. [20][21][22] Smith and Rubin had shown that in the control of lightly damped oscillatory systems, the time delay when used in the controller may cancel the effect of oscillatory complex poles and produce a deadbeat response in Tallman and Smith 23 and Rubin. 24 Suh and Bien introduced a control design called ''proportional minus delay controller'' to improve the performance of the system based on the approximation and numerical simulation in Suh and Bien.…”