Uniform Global Asymptotic Stabilization of Semilinear Periodic Discrete-Time Systems
| Autor: | Vasilii Zaitsev, Michal Niezabitowski, Evgenii Makarov, Adam Czornik, Svetlana Popova |
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| Rok vydání: | 2022 |
| Předmět: |
Lyapunov function
Zero (complex analysis) State (functional analysis) Stability (probability) Computer Science Applications symbols.namesake Discrete time and continuous time Control and Systems Engineering Control system Converse symbols Applied mathematics Lyapunov theorem Electrical and Electronic Engineering Mathematics |
| Zdroj: | IEEE Transactions on Automatic Control. 67:3598-3605 |
| ISSN: | 2334-3303 0018-9286 |
| Popis: | Semi-linear 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 semi-linear 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 (non-asymptotic) stability is proved for complex and real linear periodic discrete-time systems. Finally, examples of using the obtained results are presented. |
| Databáze: | OpenAIRE |
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