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

In this paper, a novel delay‐dependent bounded real criterion and an improved sufficient condition are derived for the design of an H_∞ state‐feedback 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. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society