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Keywords = Grönwall constraints

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18 pages, 424 KiB  
Article
Finite-Time Stability of Fractional-Order Switched Systems Based on Lyapunov Method
by Tian Feng, Lizhen Wang and Yangquan Chen
Fractal Fract. 2025, 9(2), 94; https://doi.org/10.3390/fractalfract9020094 - 2 Feb 2025
Viewed by 641
Abstract
This paper investigates the finite-time stability of a class of fractional-order switched systems with order 0<α<1, employing the fractional Lyapunov direct method. First, based on the Mittag-Leffler function and Gronwall inequality, two corresponding sufficient conditions are presented to [...] Read more.
This paper investigates the finite-time stability of a class of fractional-order switched systems with order 0<α<1, employing the fractional Lyapunov direct method. First, based on the Mittag-Leffler function and Gronwall inequality, two corresponding sufficient conditions are presented to ensure the finite-time stability of the considered system. Second, in consideration of the effectiveness of dwell time technique in switched systems, a sufficient condition is derived under a minimum average dwell time constraint. Finally, numerical simulations are performed to validate the effectiveness of the theoretical formulation. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Chaotic and Complex Systems)
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10 pages, 296 KiB  
Article
Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls
by Gafurjan Ibragimov, Ikrombek Yusupov and Massimiliano Ferrara
Mathematics 2023, 11(2), 374; https://doi.org/10.3390/math11020374 - 10 Jan 2023
Cited by 1 | Viewed by 1858
Abstract
We studied a simple motion differential game of two pursuers and one evader in R2. The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the [...] Read more.
We studied a simple motion differential game of two pursuers and one evader in R2. The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players. Full article
(This article belongs to the Section E5: Financial Mathematics)
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