Input-to-state stability for switched systems with unstable subsystems: A hybrid Lyapunov construction

2014 ◽  
Author(s):  
Guosong Yang ◽  
Daniel Liberzon
Keyword(s):  
Switched Systems ◽  
Unstable Subsystems

Stability of a class of nonlinear fractional order impulsive switched systems

2016 ◽  
Vol 39 (5) ◽  
pp. 781-790 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems ◽  
The Stability ◽  
Work First ◽  
Periodic Switching

This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.

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.

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