On piecewise quadratic Lyapunov functions for piecewise affine models of gene regulatory networks

A piecewise affine (PWA) model of a gene regulatory network is considered. After an introduction to the model, the problem of finding a generally non-smooth function V (x) which is non increasing along the system trajectories is addressed and a way of solving it is given in terms of an LMI's feasibility problem. The presence of sliding modes in the system is explicitly considered and conditions of non-increase of V(x) along these are stated in terms of LMIs. Finally, we present an example which show the resulting V (x) obtained by solving the feasibility problem described.