LMIs for delay-independent properties of delay systems and input-output analysis of systems with complex parameter

Focuses on delay-independent input-output properties (passivity, H_∞ performance, circle criterion, Popov criterion) of delay systems. The main results show that, as it is the case for the usual, rational, systems, these properties may be characterized by solvability of some linear matrix inequalities. The latter are constructed by use of some quadratic Lyapunov-Krasovskii functionals, generalizing a well-known class. The method also applies to the analysis of systems with uncertain complex parameter, for which the results are related to the search for polynomial parameter-dependent Lyapunov functions. Illustrative examples are provided.