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.

scholarly journals Input–output linearization of non-linear time-varying delay systems: the single-input single-output case

2019 ◽  
Vol 37 (3) ◽  
pp. 831-854
Author(s):  
Ihab Haidar ◽  
Florentina Nicolau ◽  
Jean-Pierre Barbot ◽  
Woihida Aggoune
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Input Output ◽  
Time Varying Delay ◽  
Output Stabilization ◽  
Non Linear ◽  
Varying Delay ◽  
Input Output Linearization

Abstract This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization are also presented. Finally, several examples illustrating our main results are discussed.

scholarly journals Exponential Stability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays via an Average Dwell-Time Method

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
N. Yotha ◽  
T. Botmart ◽  
T. Mouktonglang
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Fast Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Unstable Subsystems

The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.

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 Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

2021 ◽  
Vol 20 ◽  
pp. 88-97
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay

2016 ◽  
Vol 40 (1) ◽  
pp. 191-201 ◽  
Author(s):  
Samah Ben Atia ◽  
Anis Messaoud ◽  
Ridha Ben Abdennour
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Operating Regime ◽  
Linear Matrix ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Time Varying Delay ◽  
Partial Models ◽  
Delay Dependent ◽  
Varying Delay

In this paper, a robust multiobserver is proposed for the state estimation of discrete-time uncertain nonlinear systems with time-varying delay. The designed multiobserver is based on the decoupled multimodel approach. Unlike the classically used multimodel structures, the decoupled multimodel provides a flexibility of modelling. Indeed, the partial models’ structures can be adapted to the complexity of the system in each operating regime, thus the partial models can be with different dimensions. Delay-dependent sufficient conditions for the synthesis of a robust multiobserver against norm-bounded parametric uncertainties and in the presence of measurement noise are established in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the designed multiobserver.

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