An LMI-Based Algorithm to Compute Robust Stabilizing Feedback Gains Directly as Optimization Variables

• 成果类型: Article
• 署名作者: Felipe, Alexandre; Oliveira, Ricardo C. L. F.
• 署名单位: Universidade Estadual de Campinas
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3038359
• 发表日期: 2021
• 页码: 4365-4370
• 关键词: Linear matrix inequalities; optimization; Linear systems; Stability criteria; robust stability; Symmetric matrices; Numerical stability; decentralized control; Linear matrix inequalities (LMIs); output-feedback; robust stabilization; state-feedback

摘要

This article addresses the problem of robust stabilization of uncertain linear systems by static state- and output-feedback control laws. The uncertainty is supposed to belong to a polytope and both continuous- and discrete-time systems are investigated. Contrarily to the main stream of the linear matrix inequality (LMI)-based robust stabilization methods available in the literature, where the product between the Lyapunov (or slack variable) and control gain matrices is transformed in a new variable, this article proposes a change of paradigm, avoiding the standard change of variables and providing synthesis conditions that deal directly with the control gain as an optimization variable. The design procedure is formulated in terms of a locally convergent iterative algorithm based on LMIs, having as main novelties the following points: Both the Lyapunov and the closed-loop dynamic matrices appear affinely in the conditions; the iterative scheme involves the slack variables only, avoiding the classic alternation between the Lyapunov matrix and the control gain; an extra degree of freedom is created in terms of an additional scalar variable, which also appears affinely in the conditions and represents a scaling on the closed-loop dynamic matrix; a smart termination for the algorithm through a stability analysis condition. Numerical experiments based on exhaustive simulations show that all these features combined provide a robust stabilization technique capable to outperform the best available methods in the literature in terms of effectiveness, being specially suitable to address static output-feedback and decentralized control problems.