Robust stability of linear time-invariant multiaffine systems

This paper presents multiaffine systems as a generalisation of widely-used polytopic ones. Multiaffine systems arise naturally in systems with products of uncertain parameters or nonlinearities. Stability of polytopic systems may usually be assessed, for instance, via well-known linear matrix inequalities; hence, as multiaffine systems may easily be bounded by a polytope, results for them are readily available. However, results exploiting only the polytopic convex hull may be conservative because multiaffine systems are, in many cases, strictly included inside its convex hull. This work presents a recursive robust stability result which exploits the multiaffine structure in order to find parameter-dependent quadratic Lyapunov functions.