A unified framework of convex stability conditions for 2-D switched systems with stable or unstable modes. (July 2022)

• Record Type: Journal Article
• Authors: Zhuang, Songlin; Shang, Xinxin; Yu, Xinghu; Gao, Huijun; Shi, Yang
• Is Part Of: Automatica. Volume 141(2022)
• Publication Date: 2022-07
• Subjects: 2-D switched systems -- Convex stability conditions -- Lifting technique -- Standard l2-gain -- Stable and unstable modes; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110264
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The discrete-time two-dimensional (2-D) switched system is a powerful tool to model many practical physical processes with abrupt changes. However, the stability analysis problem for 2-D switched systems struggles to provide a unified framework for stable or unstable modes. Users have to delicately tune lots of parameters to shape the Lyapunov function for each mode. Besides, the resulting stability conditions are non-convex and thus the feasibility highly depends on the tuning parameters. In this paper, we propose a unified stability framework for 2-D switched systems, formulated by the well-known Fornasini–Marchesini local state-space model and the Roesser model. The concepts called unit switching sequence (USS) and sequence generator are presented. A novel Lyapunov function is also accordingly established which views the switching sequence as a concatenation of USSs, different from the perspective that regards the switching sequence as a combination of subsystems in previous literatures. Upon this framework, a convex stability criterion is developed, and the conservativeness can be lowered by a lifting technique at the expense of a higher off-line computational complexity. The derived theories are further extended for a standard l 2 -gain which is achieved under restricted switching signals for the first time. Numerical examples are provided for validity verification, conservativeness comparison, and l 2 -gain computation.