Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback
| Autor: | Svetlana Popova, Michal Niezabitowski, Evgenii Makarov, Vasilii Zaitsev, Adam Czornik |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Lyapunov function
General Computer Science Linear system Diagonalizable matrix Free system General Engineering Linear discrete time-varying input-output systems Lyapunov spectrum pole assignment problem TK1-9971 Controllability uniform consistency symbols.namesake local assignability static output feedback Exponential stability Discrete time and continuous time Consistency (statistics) symbols Applied mathematics General Materials Science Electrical engineering. Electronics. Nuclear engineering Mathematics |
| Zdroj: | IEEE Access, Vol 9, Pp 134174-134191 (2021) |
| ISSN: | 2169-3536 |
| Popis: | We consider a linear discrete time-varying input-output system. Our goal is to study the problem of local assignability of the Lyapunov spectrum by static output feedback control. To this end we introduce the notion of uniform consistency for discrete-time linear systems which is the extension of the notion of uniform complete controllability to input-output systems. The property of uniform consistency is investigated, some necessary and sufficient conditions for this property are obtained. The notion of uniform local attainability is introduced for the closed-loop system. We prove that uniform consistency implies uniform local attainability of the closed-loop system. The property of local Lyapunov reducibility is introduced for the closed-loop system. We prove that uniform local attainability implies local Lyapunov reducibility. We prove that, for a locally Lyapunov reducible system, the Lyapunov spectrum is locally assignable, if the free system is diagonalizable or regular (in the Lyapunov sence) or has the stable Lyapunov spectrum. |
| Databáze: | OpenAIRE |
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