Linear systems with commensurate time delays: stability and stabilization independent of delay

Pseudorational Impulse Responses — Algebraic System Theory for Distributed Parameter Systems

“…A typical algebraic approach toward this system is that of systems over rings, e.g., [6], [9]. Writing (σx)(t) for x(t − 1), (1) becomeṡ…”

Pole placement controllers for linear time-delay systems with commensurate point delays

“…The control law obtained from the above controllers becomes [6,12,13,16,17], to achieve prefixed suitable either delay-independent or delay-dependent closed-loop spectrum. This more general problem statement may be beneficial in some applications where the suitable closed-loop spectrum is reallocated, but still delaydependent, due to the intrinsic delayed nature of the original open-loop plant [3,4,18].…”

“…Time-delay systems have received an increasing interest in the last years (see, for instance, [2,3,4,5,6,7,12,13,15,17,18,20,21] since, apart from their inherent theoretical interest, they are also of interest in practical applications like, for instance, transmission lines, dynamics of fluids, or population growth rules [3,4,18]. One of the main characteristics of such systems is that they are infinite dimensional [4,6,7,12,13,17], making the controller design more complex than for the delay-free case [2,6,12,13,15,17,20,21].…”

“…One of the main characteristics of such systems is that they are infinite dimensional [4,6,7,12,13,17], making the controller design more complex than for the delay-free case [2,6,12,13,15,17,20,21]. Closed-loop stabilization may be achieved through memoryless controllers (see, for instance, [13,20]) when the plant delayed dynamics is sufficiently small.…”

Applied Interval Computation: A New Approach for Time-Delays Systems Analysis

“…A recurring subject of research is the stability or robust stability, and has undergone a notable development both conceptually and computationally (see e.g. [4], [9], [14], [15], [23], [26], [29], and references therein). Using different theoretical approaches, numerical methods and algorithms obtained are generally semi-analytic, with sometimes difficulties of implementation.…”