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 Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

2017 ◽  
Vol 15 (1) ◽  
pp. 1635-1648 ◽  
Author(s):  
Hao Xing ◽  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Finite Time Boundedness

Abstract This paper considers the guaranteed cost finite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and sufficient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the effectiveness of the proposed method.

scholarly journals L1 Input-Output Finite-Time Control of Positive Switched Nonlinear Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Bo Fan ◽  
Zhumu Fu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Distributed Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Input Output ◽  
Positive Type ◽  
Time Control

In this paper, the problem of L1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated. Nonlinear functions considered in this paper are located in a sector field. Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L1 input-output finite-time stability (L1 IO-FTS) is firstly introduced. Then, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L1 IO-FTS. Such conditions can be easily solved by linear programming. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Finite-time stability and asynchronously switching control for a class of time-varying switched nonlinear systems

2019 ◽  
Vol 42 (6) ◽  
pp. 1215-1224
Author(s):  
Ronghao Wang ◽  
Jianchun Xing ◽  
Zhengrong Xiang ◽  
Qiliang Yang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Dwell Time ◽  
Autonomous Systems ◽  
Average Dwell Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Control Lyapunov Function ◽  
Finite Time Stability

Finite-time stability and stabilization for switched nonlinear systems has been investigated in the paper. Based on existing works, we find that related results on autonomous switched nonlinear systems cannot be simply extended to non-autonomous systems. A sufficient condition has been proposed for this class of systems using the average dwell time method. Specifically, a control Lyapunov function approach is employed to stabilize the system and the finite-time controller is designed using a small control property. In contrast to autonomous switched systems, a finite-time stabilizer is constructed for time-varying switched nonlinear systems, even under the situation in which the switching mode is different between the system and the controller. Furthermore, the relation between the settling time and the average dwell time has been revealed. Finally, an example case is presented for the obtained result.

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 Robust Asynchronous H∞ Observer-Based Control Design for Discrete-Time Switched Singular Systems with Time-Varying Delay and Sensor Saturation: An Average Dwell Time Approach

Electronics ◽  
2021 ◽  
Vol 10 (19) ◽  
pp. 2334
Author(s):  
Mohamed Amin Regaieg ◽  
Mourad Kchaou ◽  
Houssem Jerbi ◽  
Attia Boudjemline ◽  
Ahmed Hafaifa
Keyword(s):  
Discrete Time ◽  
Dwell Time ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
Varying Delay

This work discuss the robust stabilization problem for discrete-time switched singular systems with simultaneous presence of time-varying delay and sensor nonlinearity. To this end, an observer-based controller was synthesized that works under asynchronous switching signals. Investigating the average dwell time approach and using a Lyapunov–Krasovskii functional with triple sum terms, sufficient conditions were derived for achieving the existence of such asynchronous controller and guaranteeing the resulting closed-loop system to be exponentially admissible with H∞ performance level. Subsequently, the effectiveness of the proposed control scheme was verified through two numerical examples.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

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