Finite-Time Control of Uncertain Linear Systems Using Statistical Learning Methods

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, we have obtained in an earlier paper, 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 attack by resorting to a statistical approach.