Convex Parameterization of Stabilizing Controllers and its LMI-based Computation via Filtering

TL;DR

This paper introduces a new convex kernel-based parameterization for stabilizing controllers, enabling efficient LMI-based computation and practical deployment, significantly improving computational speed over existing methods.

Contribution

It proposes a novel kernel Youla parameterization that simplifies stability constraints into a single affine form, leading to an efficient LMI-based approach for controller design.

Findings

LMI-based method is significantly faster than previous approaches.

The approach guarantees full-order stabilizing controllers.

Numerical experiments confirm practical efficiency and scalability.

Abstract

Various new implicit parameterizations for stabilizing controllers that allow one to impose structural constraints on the controller have been proposed lately. They are convex but infinite-dimensional, formulated in the frequency domain with no available efficient methods for computation. In this paper, we introduce a kernel version of the Youla parameterization to characterize the set of stabilizing controllers. It features a single affine constraint, which allows us to recast the controller parameterization as a novel robust filtering problem. This makes it possible to derive the first efficient Linear Matrix Inequality (LMI) implicit parametrization of stabilizing controllers. Our LMI characterization not only admits efficient numerical computation, but also guarantees a full-order stabilizing dynamical controller that is efficient for practical deployment. Numerical experiments demonstrate that our LMI can be orders of magnitude faster to solve than the existing closed-loop parameterizations.