Parametric Lyapunov functions for uncertain systems: the multiplier approach

In this chapter, we propose to use a parametric multiplier approach to deriving parametric Lyapunov functions for robust stability analysis of linear systems involving uncertain parameters. This new approach generalizes the traditional multiplier approach used in the absolute stability literature where the multiplier is independent of the uncertain parameters. Our main result provides a general framework for studying multiaffine Lyapunov functions. We show that these Lyapunov functions can be found using linear matrix inequality (LMI) techniques. Some known results on parametric Lyapunov functions are shown to be our special cases.