Stabilization of Discrete-Time Switched Nonlinear Systems

• 成果类型: Article
• 署名作者: Deaecto, Grace S.; Astolfi, Alessandro
• 署名单位: Universidade Estadual de Campinas; Imperial College London; University of Rome Tor Vergata
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3574371
• 发表日期: 2025
• 关键词: linear-systems; Sufficient condition; H-INFINITY; STABILITY; stabilizability

摘要

The stabilization problem for discrete-time switched nonlinear systems is studied under two different scenarios: time-dependent switching (open-loop control) and state-dependent switching (closed-loop control). In the first, global asymptotic stability of the zero equilibrium and a guaranteed performance are ensured by a switching rule subject to a persistent dwell time condition. In the second, a state-dependent switching function is designed to accomplish the same goals of stability and performance by means of conditions expressed in terms of a nonlinear version of the well-known Lyapunov-Metzler inequalities. A numerical method that applies to a subclass of nonlinear systems is proposed. It is able to check locally the sufficient conditions through the solution of a convex programming problem expressed by linear matrix inequalities. Academic examples illustrate the theoretical results.