Exponential stabilization and L2 -gain for uncertain switched nonlinear systems with interval time-varying delay

2016 ◽  
Vol 39 (13) ◽  
pp. 3836-3854 ◽  
Author(s):  
Yali Dong ◽  
Tianrui Li ◽  
Shengwei Mei
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Interval Time ◽  
Time Varying Delay ◽  
Varying Delay ◽  
L2 Gain

scholarly journals Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Yali Dong ◽  
Shengwei Mei ◽  
Xueli Wang
Keyword(s):  
Nonlinear Systems ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Riccati Differential Equations ◽  
Continuous State ◽  
Varying Delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is considered in the paper. By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.

scholarly journals H∞ Control for Mixed-Mode Based Switched Nonlinear Systems with Time-Varying Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhen Liu ◽  
Shu Miao ◽  
Canbo Ye ◽  
Xingbo Liu
Keyword(s):  
Nonlinear Systems ◽  
Mixed Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Control Analysis ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Mixed Modes ◽  
Varying Delay

This paper investigated H∞ performance of the switched nonlinear systems with time-varying delay, which contains mixed modes, important characteristics of switched delay systems. Most of the references ignored the existence of mixed modes in such systems, which is a fatal mistake. This paper will correct the mistake of the existing references. The mixed modes give the H∞ control for switched nonlinear delay systems a challenge. With this difficulty, we take measures to handle the effects of mixed modes on such systems and achieve the H∞ performance of such systems. Firstly, the H∞ control analysis is divided into two cases, and the sufficient conditions for the exponential decay of the Lyapunov-Krasovskii functionals are given with the integral interval approach. Secondly, the combination of average dwell-time approach and subsystem activation rate is utilized to achieve the H∞ performance for the mixed-mode based switched systems with time-varying delay. Finally, simulation examples show the efficiency of the switching control strategy.

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