A General Optimization Approach to Enlarge the Region of Attraction of Saturating Discrete-Time Delayed Systems

Silva, Romulo J.; Leite, Valter J. S.; Silva, Luís F. P.

doi:10.1007/978-3-031-10047-5_41

Cited by 1 publication

(2 citation statements)

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“…We use the L-K candidate function to characterize the estimate region of attraction, R E . This characterization is adapted from the methodology proposed in (Silva Jr. et al, 2022), such that, if V (x k ) is an L-K function, then we characterize the set R E as L V (η), where:…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…Inspired by the approach from De Souza et al (2019) and Silva et al (2018a), the authors in (Alves Lima et al, 2021) map the a Lyapunov-Krasovskii function into an augmented space to explore better optimization methods to enlarge the estimate region of attraction in the (local) robust stability analysis case. The advantage in this case is that the LMI conditions for designing the controller remains with numerical complexity independent of the maximum delay, d. This very same idea was developed independently in (Silva Jr. et al, 2022) for a different Lyapunov-Krasovskii functional. However, only the precisely known case is addressed in (Alves Lima et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Regional ISS Stabilization of Saturating State-Delayed Discrete-Time Systems

Romulo J. Silva Jr.,

Valter J. S. Leite,

Luís F. P. Silva

2022

Procedings Do XXIV Congresso Brasileiro De Automática

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Recent works in the literature deal with efficient numerical conditions to robustly stabilize state-delayed discrete-time systems under saturating actuators. However, practical issues such as the rejection of exogenous signals and their effects on the region of safe initial conditions have not been thoroughly investigated. This work extends a previous controller design condition to handle the ℓ 2 gain between the exogenous signals and the measured output. Moreover, the notion of input-to-state stability is applied, allowing to consider the effects of the disturbance signals over the estimates of the safe initial conditions region. Furthermore, a recent optimization procedure formulated in an augmented space is applied, allowing better estimates of the region of safe initial conditions while maintaining the numerical complexity acceptable. A numerical example illustrate the methods proposed and compare the achievements with the concerned literature.

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Section: Preliminary Resultsmentioning

confidence: 99%