Unified stability criteria for slowly time-varying and switched linear systems. (October 2018)

• Record Type: Journal Article
• Authors: Gao, Xiaobin; Liberzon, Daniel; Liu, Ji; Başar, Tamer
• Is Part Of: Automatica. Volume 96(2018)
• Page Start: 110
• Page End: 120
• Publication Date: 2018-10
• Subjects: Slowly time-varying systems -- Switched systems -- Linear systems -- Stability; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.06.025
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper presents a unified approach to formulating stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrix-valued functions. Using this generalized concept, a result extending existing stability conditions for slowly time-varying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result.