Uniform Global Asymptotic Stabilization of Semilinear Periodic Discrete-Time Systems

• 成果类型: Article
• 署名作者: Czornik, Adam; Makarov, Evgenii; Niezabitowski, Michal; Popova, Svetlana; Zaitsev, Vasilii
• 署名单位: Silesian University of Technology; National Academy of Sciences of Belarus (NASB); Institute of Mathematics of the National Academy of Sciences of Belarus; Udmurt State University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3105648
• 发表日期: 2022
• 页码: 3598-3605
• 关键词: Discrete-time systems; asymptotic stability; Stability criteria; Eigenvalues and eigenfunctions; Time-varying systems; Linear matrix inequalities; licenses; discrete-time systems; periodic systems; semilinear systems; State feedback; uniform global asymptotic stabilization

摘要

Semilinear discrete-time control systems with periodic coefficients are considered. The problem of uniform global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has a Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic semilinear discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Moreover, the converse Lyapunov theorem on Lyapunov (nonasymptotic) stability is proved for complex and real linear periodic discrete-time systems. Finally, examples of using the obtained results are presented.