2015/03/25 by Seungil You, You, Seungil, Ather Gattami +3
Decision Sciences · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Sparse and Compressive Sensing Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1503.07561
openalex publication_date 2015/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper reformulates and streamlines the core tools of robust stability and performance for LTI systems using now-standard methods in convex optimization. In particular, robustness analysis can be formulated directly as a primal convex (semidefinite program or SDP) optimization problem using sets of gramians whose closure is a semidefinite cone. This allows various constraints such as structured uncertainty to be included directly, and worst-case disturbances and perturbations constructed directly from the primal variables. Well known results such as the KYP lemma and various scaled small gain tests can also be obtained directly through standard SDP duality. To readers familiar with robustness and SDPs, the framework should appear obvious, if only in retrospect. But this is also part of its appeal and should enhance pedagogy, and we hope suggest new research. There is a key lemma proving closure of a grammian that is also obvious but our current proof appears unnecessarily cumbersome, and a final aim of this paper is to enlist the help of experts in robust control and convex optimization in finding simpler alternatives.