An improved delay‐dependent bounded real lemma (BRL) and H_∞ controller synthesis for linear neutral systems

Abstract

In this paper, a novel delay-dependent bounded real criterion and an improved sufficient condition are derived for the design of an H ∞ statefeedback controller for linear neutral time-delay systems. On the basis of an augmented Lyapunov-Krasovskii functional, a new bounded real lemma is introduced in terms of a convex linear matrix inequality (LMI) condition that can be solved using interior point algorithms. The bounded real lemma is extended to obtain a sufficient condition for the existence of a delay-dependent H ∞ memoryless state-feedback controller. Neither any model transformation nor bounding of any of the cross terms are utilized while deriving the bounded real lemma. Moreover, the use of any free slack matrix variable approach is avoided to a certain extent in order not to increase the complexity of the synthesis problem. A cone complementary nonlinear minimization algorithm is employed to achieve a feasible solution set for the synthesis conditions. Finally, seven numerical examples are given to illustrate the effectiveness of the proposed method.

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

“…From this point of view, researchers in the time‐delay systems community have considered plenty of different approaches such as employing various model transformations, utilizing better bounding techniques for cross terms, applying Jensen‐type integral inequalities, introducing free‐weighting matrices with Newton–Leibniz relation, exploiting full information on the relationship among the delay related terms, proposing discretized or augmented Lyapunov–Krasovskii (L‐K) functional, and decomposing the delay interval uniformly/nonuniformly into equidistant/variable subintervals. Among them, the most relaxed results have usually been obtained with the last three techniques, namely with the method of exciting full information on the delay related terms, such as in , and the use of discretized or augmented form of L‐K functional such as in , and finally the utilization of delay partitioning technique such as in . Especially, in the last decade, there is a considerable amount of research effort in the literature for the analysis and design of robust or H ∞ controllers both for continuous and discrete time‐delay systems.…”