PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME

2008 ◽  
Vol 2 (3) ◽  
pp. 192-197 ◽  
Author(s):  
Guisheng Zhai ◽  
Bo Hu ◽  
Kazunori Yasuda ◽  
Anthony N. Michel
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Average Dwell Time

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.

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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