Exponential Stabilization of Unstable Bilinear Systems in Finite- and Infinite-Dimensional Spaces

• 成果类型: Article
• 署名作者: Ouzahra, Mohamed
• 署名单位: Sidi Mohamed Ben Abdellah University of Fez
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3056579
• 发表日期: 2021
• 页码: 5982-5989
• 关键词: Nonlinear systems; control systems; Aerospace electronics; switches; Feedback control; asymptotic stability; Thermal stability; Bilinear systems; exponential stabilization; global stabilization; unstable open loop

摘要

This article discusses the uniform exponential stabilization of bilinear systems with multiplicative control inputs. We first consider the case of finite-dimensional bilinear systems, and we present stabilization results concerning the case of open-loop stable systems using a bang-bang feedback control. For open-loop unstable systems, a normalized quadratic time-varying feedback control is proposed. These results are then applied to infinite-dimensional case. Necessary and sufficient conditions are formulated in terms of unique continuation properties and integral estimates involving the control operator and the state of the uncontrolled system. Applications to finite-dimensional systems and coupled partial differential equations (PDE) are further provided.