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.
Finite-Time Stability, LMIs, Disturbance Rejection, Statistical Learning Control
Abdallah, Chaouki T.. "Finite-Time Control of Uncertain Linear Systems Using Statistical Learning Methods." (2012). https://digitalrepository.unm.edu/ece_fsp/147