LMI based robust stability conditions for linear uncertain systems: a numerical comparison

In the paper, several numerical experiments are performed in order to compare three linear matrix inequalities based sufficient conditions for the robust stability of linear systems in polytopic domains. The conditions are the quadratic stability and two robust stability conditions based on parameter dependent Lyapunov functions: one using extra variables and augmented equations and the other using a larger number of equations. From the examples, it is possible to infer about the conservativeness of the conditions and also about the cases in which an equivalence exists. Both continuous-time and discrete-time systems are investigated.