Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties

2016 ◽  
Vol 62 ◽  
pp. 129-136 ◽  
Author(s):  
Xingwen Liu ◽  
Jun Cheng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Switched Nonlinear Systems

scholarly journals On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Switched Systems ◽  
Multiple Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Arbitrary Switching ◽  
Aggregation Techniques ◽  
Robust Stability Analysis

This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

scholarly journals Adaptive Neural Tracking Control for Discrete-Time Switched Nonlinear Systems with Dead Zone Inputs

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Jidong Wang ◽  
Lengxue Zhu ◽  
Xiaoping Si
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Control ◽  
Closed Loop ◽  
Dead Zone ◽  
Switched Nonlinear Systems ◽  
Closed Loop System ◽  
Neural Controllers ◽  
Arbitrary Switching

In this paper, the adaptive neural controllers of subsystems are proposed for a class of discrete-time switched nonlinear systems with dead zone inputs under arbitrary switching signals. Due to the complicated framework of the discrete-time switched nonlinear systems and the existence of the dead zone, it brings about difficulties for controlling such a class of systems. In addition, the radial basis function neural networks are employed to approximate the unknown terms of each subsystem. Switched update laws are designed while the parameter estimation is invariable until its corresponding subsystem is active. Then, the closed-loop system is stable and all the signals are bounded. Finally, to illustrate the effectiveness of the proposed method, an example is employed.

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