Common and multiple Lyapunov functions in stability analysis of nonlinear switched systems

2012 ◽  
Author(s):  
S. N. Vassilyev ◽  
A. A. Kosov
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Nonlinear Switched Systems

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

scholarly journals Almost Global Stability of Nonlinear Switched Systems with Time-Dependent Switching

2018 ◽  
Author(s):  
Ozkan Karabacak ◽  
Aysegul Kivilcim ◽  
Rafael Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Multiple Lyapunov Functions ◽  
Koopman Operator ◽  
Nonlinear Switched Systems

For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of a common Lyapunov density for a nonlinear switched system implies almost global stability, in the same way as a common Lyapunov function implies global stability for nonlinear switched systems. In this work, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell-time constraint with an arbitrarily small dwell time. As a straightforward extension of this result, we employ multiple Lyapunov densities in analogy with the role of multiple Lyapunov functions for the global stability of switched systems. This gives rise to a minimum dwell time estimate to ensure almost global stability of nonlinear switched systems, when a common Lyapunov density does not exist. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time non-autonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator.

Stability analysis of some classes of nonlinear switched systems with time delay

2017 ◽  
Vol 48 (10) ◽  
pp. 2111-2119 ◽  
Author(s):  
Alexander Aleksandrov ◽  
Elena Aleksandrova ◽  
Alexei Zhabko
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Switched Systems ◽  
Nonlinear Switched Systems
Sign in / Sign up

Export Citation Format

Share Document