Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

We present a robust recursive framework for the regulation of discrete-time linear systems subject to polytopic uncertainties. Based on regularized least-squares with a penalty parameter, we formulate a convex optimization problem and weight the polytope vertices altogether. In this sense, the main contribution of this paper consists of a robust recursive framework for the computation of stabilizing feedback gains. The solution does not require numerical optimization packages and relies ultimately on a single penalty parameter which is easily tuned. Moreover, the gains are obtained recursively through algebraic expressions, as opposed to related works which employ linear matrix inequalities. Under observability and controllability conditions, we demonstrate convergence and stability of the closed-loop system in terms of an algebraic Riccati equation. We provide numerical and real-world examples to validate the proposed approach and for comparison with a robust
$H_{\infty }$
controller.