Further Results on the Control Law via the Convex Hull of Ellipsoids

• 成果类型: Article
• 署名作者: Nguyen, Hoai-Nam
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3335827
• 发表日期: 2024
• 页码: 2753-2760
• 关键词: Ellipsoids; Lyapunov methods; optimization; Convex functions; Linear matrix inequalities; discrete-time systems; Time-varying systems; Convex hull of ellipsoids; invariant set; linear matrix inequality (LMI); Lyapunov function; uncertain and/or time-varying linear discrete-time system

摘要

Recently, a new Lyapunov function based on the convex hull of ellipsoids was introduced for the study of uncertain and/or time-varying linear discrete-time systems with/without constraints. The new Lyapunov function has many attractive features such as: 1) the associated ellipsoids are not required to be robustly invariant; 2) the design conditions are formulated as linear matrix inequality constraints. The control law is obtained by solving a convex optimization problem online. This optimization problem generally does not have a closed-form solution, and hence it is solved by numerical methods. In this article, we intend to complement the results by analyzing the geometric structures of the solution to the optimization problem, and of the control law. In particular, we show that the control law is a piecewise linear and Lipschitz continuous function of the state.