A polynomial blossoming approach to stabilization of periodic time-varying systems. (July 2022)

• Record Type: Journal Article
• Authors: Xie, Xiaochen; Lam, James; Fan, Chenchen; Wang, Xiaomei; Kwok, Ka-Wai
• Is Part Of: Automatica. Volume 141(2022)
• Publication Date: 2022-07
• Subjects: Blossoming -- Matrix polynomials -- Periodic systems -- Stabilization -- Time-varying systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110305
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper proposes a novel polynomial blossoming approach to designing stabilizing controller for a class of periodic time-varying systems. Utilizing multi-convexity of a non-homogeneous symmetric matrix polynomial, the approach can provide a series of convex optimization conditions to guarantee the negativity/positivity of matrix polynomial. Special cases of the proposed approach are also discussed, giving the conclusion that our approach generalizes two existing matrix polynomial approaches. For periodic systems formulated with [ 0, 1 ] -bounded time-varying coefficients, the designed stabilizing controller not only involves user-selectable varying gains over time intervals that are possibly non-identical to the system fundamental period, but can also guarantee the exponential stability of the closed-loop system. The effectiveness of our approach is validated and illustrated through two application-oriented simulation examples.