S-procedure for the analysis of control systems with parametric uncertainties via parameter-dependent Lyapunov functions

In this paper, the problem of robust stability of systems subject to parametric uncertainties is considered. Sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than Popov's stability criterion. It is shown how the so-called S-procedure plays a crucial role in the derivation of this criterion. A comparison with existing stability criteria is done. An equivalent frequency-domain criterion is given. Extensions to cover slowly time-varying systems and robust performance are given.