  We propose a counter-example guided inductive synthesis (CEGIS) scheme for
the design of control Lyapunov functions and associated state-feedback
controllers for linear systems affected by parametric uncertainty with
arbitrary shape. In the CEGIS framework, a learner iteratively proposes a
candidate control Lyapunov function and a tailored controller by solving a
linear matrix inequality (LMI) feasibility problem, while a verifier either
falsifies the current candidate by producing a counter-example to be considered
at the next iteration, or it certifies that the tentative control Lyapunov
function actually enjoys such feature. We investigate the Lipschitz continuity
of the objective function of the global optimization problem solved by the
verifier, which is key to establish the convergence of our method in a finite
number of iterations. Numerical simulations confirm the effectiveness of the
proposed approach.
