scholarly journals Stability Analysis of a Class of Switched Nonlinear Systems with an Improved Average Dwell Time Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongwei Guo
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Asymptotically Stable ◽  
Switched Nonlinear Systems ◽  
Globally Asymptotically Stable ◽  
Unstable Subsystems ◽  
Average Dwell Time Method ◽  
The Stability

This paper investigates the stability of switched nonlinear (SN) systems in two cases: (1) all subsystems are globally asymptotically stable (GAS), and (2) both GAS subsystems and unstable subsystems coexist, and it proposes a number of new results on the stability analysis. Firstly, an improved average dwell time (ADT) method is presented for the stability of such switched system by extending our previous dwell time method. In particular, an improved mode-dependent average dwell time (MDADT) method for the switched systems whose subsystems are quadratically stable (QS) is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results to the stability analysis are obtained. It should be pointed out that the obtained results have two advantages over the existing ones; one is that the improved ADT method simplifies the conditions of the existing ADT method, the other is that the obtained lower bound of ADT (τa*) is also smaller than that obtained by other methods. Finally, illustrative examples are given to show the correctness and the effectiveness of the proposed methods.

H∞ control for a class of continuous-time switched systems with state constraints via a mode-dependent switching method

2018 ◽  
Vol 40 (11) ◽  
pp. 3358-3367 ◽  
Author(s):  
Qingyu Su ◽  
Haichao Zhu ◽  
Jian Li
Keyword(s):  
Switched Systems ◽  
Dwell Time ◽  
State Feedback ◽  
State Constraints ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Globally Asymptotically Stable ◽  
Average Dwell Time Method ◽  
Linear State ◽  
Switching Method

In this paper, the H∞ control problem for linear state-constrained switched systems via the improved mode-dependent average dwell time method is investigated. Using this proposed method, which considers different decay rates of a Lyapunov function related to an active subsystem on the basis of whether there is saturation or not, the resulting minimum admissible mode-dependent average dwell time is smaller than that of the traditional average dwell time method, which assumes a constant decay rate, regardless of whether there is saturation or not. Thus, this method is less conservative than the traditional average dwell time method. In addition, this paper outlines the design of the state feedback controller of the switched systems, which guarantees that the closed-loop linear state-constrained switched system is globally asymptotically stable and obtains a weighted L2 gain. The availability and applicability of the proposed method are shown by the application of a boost converter.

scholarly journals ISS and integral-ISS of switched systems with nonlinear supply functions

2021 ◽  
Author(s):  
Shenyu Liu ◽  
Aneel Tanwani ◽  
Daniel Liberzon
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Activation Time ◽  
Unstable Subsystems ◽  
Supply Functions ◽  
Dissipation Inequalities ◽  
Integral Version

AbstractThe problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results.

scholarly journals Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

2021 ◽  
Author(s):  
Ran Yang ◽  
Song Liu ◽  
Xiaoyan Li ◽  
Jian Xiao
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Stability Conditions ◽  
Razumikhin Technique ◽  
Unstable Subsystems ◽  
Slow Switching

Abstract This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

scholarly journals Stabilization of a Class of Continuous-Time Switched Systems with State Constraints via a Mode-Dependent Switching Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qingyu Su ◽  
Peipei Wang
Keyword(s):  
Continuous Time ◽  
Switched Systems ◽  
Dwell Time ◽  
State Constraints ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Average Dwell Time Method ◽  
The Stability ◽  
Switching Method

The stability and the stabilization problems for a class of continuous-time switched systems with state constraints via a mode-dependent switching method are investigated. The paper presents an improved average dwell time method, which considers different decay rates of a Lyapunov function related to each of the active subsystems according to whether the saturations occur or not, respectively. It is shown that the improved average dwell time method is less conservative than the common average dwell time method. Based on the improved average dwell time method, the sufficient conditions and state feedback controllers for stabilization of the switched system are derived. A numerical example is given to illustrate the proposed approach.

Stability and Stabilization of Heterogeneous Switched Systems with Mode-Dependent Average Dwell Time via Homogeneous Polynomial Lyapunov Functions Approach

2020 ◽  
Vol 29 (16) ◽  
pp. 2050258
Author(s):  
Shaohang Yu ◽  
Chengfu Wu ◽  
Liang Wang ◽  
Jia-Nan Wu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Homogeneous Polynomial ◽  
Stability Property ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Stability And Stabilization ◽  
The Stability

This work researches the problem of searching for multiple homogeneous polynomial Lyapunov functions (HPLFs) for heterogeneous switched linear systems. First, a nonconvex optimization condition is constructed to study the stability property of heterogeneous switched systems, where each Lyapunov function candidate reduces dimension to their corresponding matrix eigenvalue. Based on the stability analysis condition, a controller-dependently multiple HPLFs condition is introduced to determine controllers and explores locally minimum mode-dependent average dwell time (LMMDADT). Additionally, the existing properties condition and solvable properties condition of controllers are given in the form of HPLFs. At last, a practical example and a contrast example are both presented to show feasibility of the proposed results.

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