Liapunov functions and stability in control theory, second ed., : A. Bacciotti, L. Rosier; Springer, Berlin, 2005, ISBN: 3-540-21332-5

is quite strange that, in this chapter, some results do concern constant delays as well. I would have preferred it considered in a separate chapter or, at least, comments and analysis could have been unified in another section. Part III (Chapter 8) concludes the book with input–output stability analysis, mainly using the small gain theorem. First the method of comparison systems (embedding the time-delay system in a delay-free one with delay feedback) allows to get a sufficient condition of input–output stability in terms of LMIs, either using the bounded real lemma on the delay-free system with feedback uncertainty or using the LK approach using model transformation. Then a time-domain approach is used to solve a scaled small gain problem. An application of these theoretical studies concerns the approximation of time-varying or distributed delays, which are modelled as feedback uncertainty. The interesting feature of this chapter is to make a connection with the H∞ approach, while remaining consistent with the objective of stability analysis only. Finally, Appendices A and B contain some useful facts on matrices and linear matrix inequalities. In conclusion, in spite of the above criticisms, I find this book well written and very interesting to read. It contains many results on stability analysis of time-delay systems and I strongly recommend it to researchers interested in analysis and control of such systems.