A note on the Lyapunov stability of linear conservative gyroscopic systems

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.

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220983637 ◽

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.

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

Symmetry ◽

10.3390/sym13071272 ◽

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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