scholarly journals Special solutions of Kirchhoff equations and their Lyapunov stability

2004 ◽  
Vol 53 (12) ◽  
pp. 4029
Author(s):  
Xue Yun ◽  
Chen Li-Qun ◽  
Liu Yan－Zhu
Keyword(s):  
Lyapunov Stability ◽  
Kirchhoff Equations ◽  
Special Solutions

Discontinuous Control and Stability Analysis of Step-Down DC-DC Voltage Converters

2020 ◽  
Vol 38 (3A) ◽  
pp. 446-456
Author(s):  
Bashar F. Midhat
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Control Method ◽  
Power Electronic ◽  
Electronic Circuits ◽  
Dc Voltage ◽  
Power Electronic Circuits ◽  
Lyapunov Stability Criterion ◽  
Control Step ◽  
Step Down

Step down DC-DC converters are power electronic circuits, which mainly used to convert voltage from a level to a lower level. In this paper, a discontinuous controller is proposed as a control method in order to control Step-Down DC-DC converters. A Lyapunov stability criterion is used to mathematically prove the ability of the proposed controller to give the desired voltage. Simulationsl1 are performedl1 in MATLABl1 software. The simulationl1 resultsl1 are presentedl1 for changesl1 in referencel1 voltagel1 and inputl1 voltagel1 as well as stepl1 loadl1 variations. The resultsl1 showl1 the goodl1 performancel1 of the proposedl1 discontinuousl1 controller.

scholarly journals Hamiltonian Aspects of Three-Layer Stratified Fluids

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni ◽  
T. T. Vu Ho
Keyword(s):  
Hamiltonian Structure ◽  
Linear Equations ◽  
Hamiltonian Formalism ◽  
Reduction Process ◽  
Ideal Fluids ◽  
Upper Lid ◽  
Stratification Structure ◽  
Special Solutions ◽  
Dispersionless Limit ◽  
Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

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