Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

• 成果类型: Article
• 署名作者: de S. Madeira, Diego
• 署名单位: Universidade Federal do Ceara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3074850
• 发表日期: 2022
• 页码: 2100-2107
• 关键词: State feedback; asymptotic stability; Output feedback; Linear systems; Lyapunov methods; Symmetric matrices; Stability criteria; Exponential QSR-dissipativity; exponential stability; State feedback; static output feedback (SOF) stabilizability

摘要

Using the notion of exponential QSR-dissipativity (i.e., dissipativity with respect to a quadratic supply rate given in terms of real matrices Q, S,R), this article presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.