Generalized Lyapunov function theorems and its applications in switched systems

2015 ◽  
Vol 77 ◽  
pp. 40-45 ◽  
Author(s):  
Qiang Yu ◽  
Baowei Wu
Keyword(s):  
Lyapunov Function ◽  
Switched Systems ◽  
Generalized Lyapunov Function

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.

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