$ {\cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

Download Full-text

Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach

Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering - Studies in Computational Intelligence ◽

10.1007/978-3-642-37781-5_7 ◽

2013 ◽

pp. 119-136 ◽

Cited By ~ 2

Author(s):

Tina Thiessen ◽

Sören Plönnigs ◽

Wolfgang Mathis

Keyword(s):

Geometric Approach ◽

Switching Behavior ◽

Electronic Circuits ◽

Fast Switching

Download Full-text

L2 Gain Performance Analysis of Periodic Linear Switched Systems

Proceedings of the 45th IEEE Conference on Decision and Control ◽

10.1109/cdc.2006.377372 ◽

2006 ◽

Cited By ~ 2

Author(s):

D. Gray Roberson ◽

Daniel J. Stilwell

Keyword(s):

Performance Analysis ◽

Switched Systems ◽

Periodic Linear ◽

L2 Gain

Download Full-text

Stabilizing Sequence Search for Time-Controlled Switched Nonlinear Systems with All Unstable Modes

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418710074 ◽

2018 ◽

Vol 18 (06) ◽

pp. 1871007

Author(s):

Jiqiang Wang

Keyword(s):

Switched Systems ◽

System Performance ◽

Numerical Study ◽

Time Sequence ◽

Duty Ratio ◽

Switching Frequency ◽

Switched Nonlinear Systems ◽

Fast Switching ◽

Sequence Search ◽

Switching Method

One of the important problems in time-controlled switched dynamical systems is to find a stabilizing time sequence if there is any. The problem is challenging for switched systems with all unstable modes. Two fundamental approaches are introduced, which are classified as the fast switching method and the method of converting state-controlled signals. Five schemes are delineated and validated in the numerical study based on the two approaches. The effects of switching frequency and duty ratio on the dynamical system performance are analyzed, from which important implications have been drawn for use in practical system design. The proposed methods shall also provide intuition into understanding the mechanism of how to maintain a dynamical system’s stability when all of its modes are unstable.

Download Full-text