"Bi-polytopic" Lyapunov functions for robust stability and fragility analysis of discrete-time models

This paper addresses the problem of analysing both robust stability and non fragility induced by a static output feedback control law. The considered models are discrete-time linear state-space representations that are subject to polytopic uncertainties. The only restriction is that the uncertainty affecting the observation matrix is independent on the uncertainty affecting evolution and control matrices. Stability is attested by the existence of a Lyapunov function that is quadratic with respect to the state vector and depends on the uncertain parameters in a "bi-polytopic way". Fragility is also handled in this paper. This works is part of LMI framework.