Improved delay-dependent bounded real lemma for uncertain time-delay systems

This paper concerns reducing the conservatism of delay-dependent bounded real lemma (BRL) of time-delay systems with uncertainty described by a linear fractional form. By introducing an augmented Lyapunov functional, an improved BRL is established in terms of linear matrix inequalities (LMIs). Theoretical comparisons show that the obtained BRL is less conservative than some previous ones and the recent results in [S.Y. Xu, L. James, Y. Zou, New results on delay-dependent robust image control for systems with time-varying delays, Automatica 42 (2006) 343–348; T. Li, L. Guo, C. Lin, Y.M. Zhang, Delay-range-dependent bounded real lemma for time-delay systems, Asian Journal of Control 10 (2008) 708–717] are actually equivalent to the special cases of the obtained BRL. Numerical examples are also given to demonstrate the effectiveness of the proposed result.