Sampled-Data Control of Nonlinear Oscillations Based on LMIs and Fridman's Method

Seifullaev, Ruslan E.; Fradkov, Alexander L.

doi:10.3182/20130703-3-fr-4039.00024

Cited by 10 publications

(13 citation statements)

References 11 publications

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“…From that theorem it was found that the pendulum system is stable with = 0.191 and 1 = −23.6, 2 = −6. It is seen that even for this special case the lower bound for the sampling frequency provided in [34] is 1/ = 5.23 Hz, which is greater than ours. However, for the case of a periodic sampling and a linear discretetime control the estimate given in [34] is better than ours: 1/0.302 = 3.31 Hz.…”

Section: Numerical Example: Mathematical Pendulumcontrasting

confidence: 64%

“…Let us compare the above result with Example 4.1 of [34], where the linear discrete-time control of (53) was treated (in our notation ( ) = , so ] 1 = ] 2 = 1). We are primarily interested in the case of a nonuniform sampling which was considered in Theorem 1 [34]. From that theorem it was found that the pendulum system is stable with = 0.191 and 1 = −23.6, 2 = −6.…”

Section: Numerical Example: Mathematical Pendulummentioning

confidence: 97%

“…The parameters of (53) are = 9.8 m/s 2 , = 1 m, = 2 kg. The function ( ) = sin is bounded and satisfies a sectoral constraint (2) with 1 = −0.2173, 2 = 1 (see [34]). Assume that the function (⋅) obeys (8) with ] 1 = 0.95, ] 2 = 1.05 (i.e., its slope can deviate as 1 ± 5%. ]…”

Section: Numerical Example: Mathematical Pendulummentioning

confidence: 99%

“…The most publications on sampled-data stabilization treat the case when the plant is linear and the discrete-time control implements the zero-order hold strategy. As for nonlinear plants (with single or multiple nonlinearities), their stabilization problem by a linear zero-order hold sampleddata control was considered in [34][35][36][37]. The technique used in these papers was based on the method of input delays and on constructing special Lyapunov-Krasovskii functionals.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

Churilov

2018

Mathematical Problems in Engineering

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Section: Numerical Example: Mathematical Pendulumcontrasting

confidence: 64%

Section: Numerical Example: Mathematical Pendulummentioning

confidence: 97%

Section: Numerical Example: Mathematical Pendulummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

Churilov

2018

Mathematical Problems in Engineering

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“…For the nonlinear multivariable Lur'e systems, estimates of the discretization step generalizing the results of [11,14] were obtained. The problems of synchronization of simple pendulums and stabilization of the pendulum on cart demonstrated essential improvement in the estimates of the discretization step as compared with the estimates obtained by other methods.…”

Section: Discussionmentioning

confidence: 99%

Linear matrix inequality-based analysis of the discrete-continuous nonlinear multivariable systems

Seifullaev

Fradkov

2015

Autom Remote Control

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The E.M. Fridman method for analysis of the hybrid linear systems by passing to a system with sawtoothed delay and using the nonstationary Lyapunov-Krasovskii functionals and descriptor variables was extended to the nonlinear multivariable Lur'e systems. Consideration was given to the discrete control in the form of a feedback with bounded above variable step of discretization. At that, in the system equations the control function was multiplied by a bounded scalar nonlinear function. This case corresponds to numerous oscillators such as the "pendulum on cart" system. On the basis of the classical results obtained by V.A. Yakubovich on losslessness of the S-procedure, the problem of estimating the upper boundary of the discretization step comes to analyzing the system of linear matrix inequalities for solvability.

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Robust nonlinear sampled‐data system analysis based on Fridman's method and S‐procedure

Seifullaev

Fradkov

2015

Intl J Robust & Nonlinear

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Summary This paper is devoted to the evaluation of sampling interval providing robust exponential stability of nonlinear system with sector‐bounded nonlinearities. It extends our previous results (R. E. Seifullaev, A. L. Fradkov. Sampled‐data control of nonlinear oscillations based on LMIs and Fridman's method. In 5th IFAC International Workshop on Periodic Control Systems, 95‐100. Caen, France. 2013). The proposed approach exploits E. Fridman's method for linear systems based on a general time‐dependent Lyapunov–Krasovskii functional. With classical results of V. A. Yakubovich about S‐procedure, the problem is reduced to feasibility analysis of linear matrix inequalities. The results are illustrated by example: the pendulum system with friction and sector‐bounded multiple nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.

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Sampled-Data Control of Nonlinear Oscillations Based on LMIs and Fridman's Method

Cited by 10 publications

References 11 publications

On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

Linear matrix inequality-based analysis of the discrete-continuous nonlinear multivariable systems

Robust nonlinear sampled‐data system analysis based on Fridman's method and S‐procedure

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