Parameter dependent Lyapunov functions for a class of uncertain linear systems: an LMI approach

The paper deals with the robust stability of linear systems with real time varying parameters with magnitude and rate of change which are confined to a given polytope. The system is described by a set of differential and algebraic equations and the system matrices may be polynomial functions of the uncertain parameters. We present LMI conditions for the construction of Lyapunov functions that depend quadratically on the uncertain parameters. The well known quadratic stability notion, based on quadratic Lyapunov functions, is also studied, connections are established and numerical examples illustrate the main results