Statistical learning methods in linear algebra and control problems: The example of finite-time control of uncertain linear systems

In this paper we show how some difficult linear algebra problems can be "approximately" solved using statistical learning methods. We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to time-varying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, the paper provides a sufficient condition for finite-time stabilization in the presence of time-varying disturbances; such condition requires the solution of a linear matrix inequality (LMI) feasibility problem, which is by now a standard application of linear algebraic methods. In the output feedback case, however, we end up with a bilinear matrix inequality (BMI) problem which we tackle by resorting to a statistical approach.