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

Abstract

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.

A less conservative stability criterion for sampled‐data system via a fractional‐delayed state and its state‐space model

“…Increasing sampling intervals leads to the low channel occupation. Therefore, sampled‐data systems have attracted considerable attention from many researchers …”

“…The second approach is based on the representation of a sampled‐data system in the form of a discrete‐time system . The third approach is based on the representation of a sampled‐data system in the form of a continuous‐time system with a delayed control input called as an input delay approach . The input delay approach is frequently used for the stability analysis.…”

“…Therefore, sampled-data systems have attracted considerable attention from many researchers. [3][4][5][6][7][8][9][10][11][12][13][14][15] There are three approaches for stability analysis of a sampled-data system. The first approach is based on the representation of the sampled-data system in the form of an impulsive model.…”

“…8,9 The third approach is based on the representation of a sampled-data system in the form of a continuous-time system with a delayed control input called as an input delay approach. [5][6][7]10,[13][14][15] The input delay approach is frequently used for the stability analysis. Based on the input delay approach, many researchers have deeply studied reducing the conservatism in the literature.…”

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

“…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.…”