D-stability analysis for discrete systems with a time delay

Guaranteed cost D-stabilization and H∞ D-stabilization for linear discrete time-delay systems

“…The linear discrete time-delay system (1) is called Dða,rÞ-stable [13], if all eigenvalues of system (1), i.e., all roots of the characteristic equation (2) are within the circle Dða,rÞ centered at a þ j0 with radius r, where jaj þ ro1.…”

D‐Stability analysis for discrete delay systems

“…Taking the absolute value of both sides of the above equation and using Lemma 1 and the properties of the matrix norm, we obtain |v|= \B\ (6) Contrary to the conclusion, we assume that v I > 1 for the solutions of (5). Because!…”

“…[8] considered the stability criteria for discrete time-delay systems, but the result is only concerned with stability analysis. Later, [6] proposed some criteria to guarantee not only stability, but also achievement of certain performance for the discrete-delay systems. That is, the criteria are proposed to ensure all the closed-loop eigenvalues of discrete-delay systems be located inside a specific disk D(a, r) centered as (a, 0) with radius r. In [6], several sufficient conditions for ensuring the Z)-stability robustness of discrete time-delay systems subjected to parametric perturbations are also presented.…”

“…That is, the criteria are proposed to ensure all the closed-loop eigenvalues of discrete-delay systems be located inside a specific disk D(a, r) centered as (a, 0) with radius r. In [6], several sufficient conditions for ensuring the Z)-stability robustness of discrete time-delay systems subjected to parametric perturbations are also presented. However, there is a serious limitation in [6]; the delay duration can only be one. Recently, Ref.…”

Sufficient Conditions for Robust Stability of Uncertain Discrete Systems With Multiple Time Delays

“…In Ref. (10) (3) where F is a constant matrix, called control gain, of appropriate dimensions. Furthermore, substituting (3) into (1) yields an uncer tain closed-loop discrete time-delay system described by (4) Then the nominal closed-loop discrete system, the sys tem in the absence of both uncertainties and time de lays, is given by (5) Before stating the problem to be tackled, we first in troduce for system (1) In this section, in terms of eigenstructure assignment we will develop a method whereby a new sufficient con dition is derived for uncertain discrete systems with multiple time delays.…”