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Rapid exponential stabilization of nonlinear continuous systems via event-triggered impulsive control

Dlala Mohsen

Demonstratio Mathematica

2022

Vol. 55, nr 1

470--481

This article investigates the problem of rapid exponential stabilization for nonlinear continuous systems via event-triggered impulsive control (ETIC). First, we propose a trigger mechanism that, when triggered by a predefined event, causes the closed-loop system exponentially stable. Then, the exponential stabilization is achieved by the designed ETIC with or without data dropout. The case where there are delays in the ETIC signals is also studied, and the exponential stabilization is proved. Finally, a numerical study is presented, along with numerical illustrations of the stability results.

On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

2015

Vol. 48, nr 3

413--423

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

Stochastic impulsive pressure calculations for time dependent human hip joint lubrication

Wierzcholski K.

Acta of Bioengineering and Biomechanics

2012

Vol. 14, no. 4

81-100

The present paper is concerned with the calculation of the stochastic unsteady, impulsive pressure distributions and load carrying capacities in human hip joint for unsteady stochastic conditions, various standard deviations and Gaussian probability density function. The total changes of hydrodynamic pressure caused by viscoelastic synovial fluid properties are completely estimated. Calculations are performed in a super thin layer of biological synovial fluid inside the slide hip joint gap limited by a spherical bone head. Using a new unified operator of summation (UOS) method, the numerical topology of pressure calculation for a difference method is applied. From numerical standpoint the proposed method of solving modified hydrodynamic equations reduces this problem to resolving the partial recurrence non-homogeneous equation of second order with variable coefficients.