Directional metric regularity of mappings and stability theorems

AbstractIn this paper, we discuss an inverse problem for the Vlasov–Poisson system. We prove local uniqueness and stability theorems by using the method in Anikonov and Amirov [Dokl. Akad. Nauk SSSR 272 (1983), 1292–1293] under the specular reflection boundary condition and with a prescribed outward electrical field at the boundary.

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The stability theorems for discrete dynamical systems on two-dimensional manifolds

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.57.403 ◽

1981 ◽

Vol 57 (8) ◽

pp. 403-407 ◽

Cited By ~ 3

Author(s):

Atsuro Sannami

Keyword(s):

Dynamical Systems ◽

Discrete Dynamical Systems ◽

Two Dimensional ◽

Stability Theorems ◽

The Stability

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Stability Theorems and Estimates of the Rate of Convergence of the Components of Factorizations for Walks Defined on Markov Chains

Theory of Probability and Its Applications ◽

10.1137/1125040 ◽

1981 ◽

Vol 25 (2) ◽

pp. 325-334 ◽

Cited By ~ 5

Author(s):

K. A. Borovkov

Keyword(s):

Markov Chains ◽

Rate Of Convergence ◽

Stability Theorems

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Robust H∞ control of neutral system for sampled-data dynamic positioning ships

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dny029 ◽

2018 ◽

Vol 36 (4) ◽

pp. 1325-1345 ◽

Cited By ~ 2

Author(s):

Minjie Zheng ◽

Yujie Zhou ◽

Shenhua Yang ◽

Lina Li

Keyword(s):

Sufficient Conditions ◽

Control Law ◽

Dynamic Positioning ◽

Neutral System ◽

Time Varying ◽

Sampled Data ◽

Stability Theorems ◽

Data Control ◽

Conservative Result ◽

Data Controller

Abstract This study focuses on the robust ${H}_{\infty }$ sampled-data control problem of neutral system for dynamic positioning (DP) ships. Using the input delay approach and a state-derivative control law, the ship DP system is turned into a neutral system with time-varying delays. By incorporating the delay-decomposition technique, Wirtinger-based integral inequality and an augmented Lyapunov–Krasovskii functional, less conservative result is derived for the resulting system. Sufficient conditions are established to determine the system’s asymptotical stability and achieve ${H}_{\infty }$ performance using Lyapunov stability theorems. Then the ${H}_{\infty }$ sampled-data controller is obtained by analyzing the stabilization conditions. Finally, simulation result is shown that the proposed method is effective.

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