scholarly journals Exponential Stabilization for a Class of Nonlinear Switched Systems with Mixed Delays under Asynchronous Switching

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yongzhao Wang
Keyword(s):  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Schur Complement ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Asynchronous Switching ◽  
Nonlinear Switched Systems ◽  
Switched Nonlinear System

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

2016 ◽  
Vol 40 (4) ◽  
pp. 1082-1091 ◽  
Author(s):  
Junqi Yang ◽  
Yantao Chen ◽  
Zheng Zheng ◽  
Wei Qian
Keyword(s):  
State Estimation ◽  
Switched Systems ◽  
Dwell Time ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Nonlinear Switched Systems ◽  
Continuous State

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

scholarly journals An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chuangxia Huang ◽  
Hanfeng Kuang ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Average Dwell Time Method ◽  
Uniformly Ultimate Boundedness

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

2021 ◽  
pp. 014233122110048
Author(s):  
Yilin Shang ◽  
Leipo Liu ◽  
Yifan Di ◽  
Zhumu Fu ◽  
Bo Fan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Current State ◽  
Guaranteed Cost ◽  
Event Triggered

This paper considers the problem of guaranteed cost and finite-time event-triggered control of fractional-order switched systems. Firstly, an event-triggered scheme including both the information of current state and an exponential decay function is proposed, and a novel cost function that adopts the characteristics of fractional-order integration is presented. Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. Meanwhile, the event-triggered parameters and state feedback gains are simultaneously obtained via solving linear matrix inequalities. Moreover, Zeno behavior does not exist by finding a positive lower bound of the triggered interval. Finally, an example about fractional-order switched electrical circuit is provided to show the effectiveness of the proposed method.

Finite-time stability and finite-time boundedness of fractional order switched systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3364-3371 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Lili Liu ◽  
Yue-E Wang ◽  
Changtao Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability and finite-time boundedness of fractional order switched systems with [Formula: see text] are investigated in this paper. First of all, by employing the average dwell time technique and Lyapunov functional method, some sufficient conditions for finite-time stability and finite-time boundedness of fractional order switched systems are proposed. Furthermore, the state feedback controllers are constructed, and sufficient conditions are given to ensure that the corresponding closed-loop systems are finite-time stable and finite-time bounded. These conditions can be easily obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness of the results.

scholarly journals Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Li ◽  
Xiaodi Li ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Method ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Nonlinear Switched Systems

This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

scholarly journals Integrated Fault Detection and Fault Tolerant Control for Switched Systems with Asynchronous Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Supeng Zhu ◽  
Haoyu Cheng ◽  
Wenxing Fu ◽  
Xiaohan Zhao ◽  
Wenyuan Li ◽  
...  
Keyword(s):  
Fault Detection ◽  
Switched Systems ◽  
Fault Tolerant ◽  
Average Dwell Time ◽  
Fault Tolerant Control ◽  
Functional Method ◽  
Linear Matrix ◽  
Asynchronous Switching ◽  
Finite Time Stability ◽  
Average Dwell Time Method

The problem of integrated fault detection and fault tolerant control for switched systems with asynchronous switching is focused on in this paper. Based on the switched model, the inherent asynchronous switching is taken into consideration. The asynchronous switching means that the switching of filters/controllers will always lag behind the switching of modes, which will degrade the performance of the closed-loop system. The Lyapunov functional method and mode-dependent average dwell time method are combined for the analysis of the finite-time stability of the switched system. The properties of each subsystem are taken into consideration, which are less conservative. To achieve optimal performance, the filters and controllers are designed simultaneously. The parameters of filters and controllers are given in the form of linear matrix inequalities. In the end, the numerical example is given to illustrate the effectiveness of the proposed method.

scholarly journals Control of Stochastic Nonlinear Switched Systems using Fuzzy Law

2021 ◽  
Vol 2050 (1) ◽  
pp. 012015
Author(s):  
Hong Yang ◽  
Yu Zhang ◽  
Chao Yang ◽  
Le Zhang
Keyword(s):  
Nonlinear System ◽  
Switched Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Simulation Software ◽  
Switching Law ◽  
Nonlinear Switched Systems ◽  
Switched Nonlinear System ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The problem about controller design for stochastic nonlinear switched systems with delay is considered. Stochastic switched nonlinear system is a kind of nonlinear system which integrates switching and nonlinear fuzzy characteristics and can fully reflect stochastic factors. First, the mathematical model of stochastic nonlinear switched systems with time delay and disturbance is given. Second, the corresponding controller is designed for the proposed model. Then, we use the multi-Lyapunov method to establish the closed-loop system on the basis of our designed controller, and give the necessary and sufficient conditions for the stability of the system. The switching law is designed to ensure the stability of subsystems activated by switching time. Finally, through the simulation software, we can see that the stability condition we obtained can make the studied system stable.

scholarly journals H∞/H− Simultaneous fault detection and control for continuous-time linear switched delay systems under asynchronous switching

2018 ◽  
Vol 41 (1) ◽  
pp. 263-275 ◽  
Author(s):  
Hossein Shokouhi-Nejad ◽  
Amir Rikhtehgar Ghiasi ◽  
Mohammad Ali Badamchizadeh ◽  
Saeed Pezeshki
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Linear Matrix ◽  
Asynchronous Switching ◽  
State Delay ◽  
Performance Indexes ◽  
And Control

In this paper, the problem of simultaneous fault detection and control for continuous-time switched state-delay systems under asynchronous switching is investigated. The aim is to design a detector/controller unit where the detector is an observer and the controller is an observer-based controller. Based on the average dwell time approach, a new method is proposed where both stability and fault detection are considered, simultaneously, through certain performance indexes. This problem is formulated as a mixed H∞/ H− problem and its solution leads to new sufficient conditions in the form of linear matrix inequality feasibility conditions. The effectiveness of the design technique is illustrated via an example.

scholarly journals Almost Global Stability of Nonlinear Switched System with Stable and Unstable Subsystems

2020 ◽  
Author(s):  
Aysegul Kivilcim ◽  
Ozkan Karabacak ◽  
Rafal Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Operation Time ◽  
Average Dwell Time ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Unstable Subsystems ◽  
The Stability ◽  
Slow Switching

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

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