Approximating Sets of Stabilizing Periodic Switching Signals

2026-01-01

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Shevchenko, Ivan O. *

Liu, Xinzhi

DOI：10.1109/LCSYS.2026.3683401

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We propose a method of approximating the set of all T -periodic globally stabilizing switching signals corresponding to a fixed switched linear system. This is accomplished by approximating system solutions using a truncated Chen-Fliess series expansion and imposing successively less restrictive conditions on the spectral radius of the approximate time- T state-transition matrix. For periodic switching signals with at most d switches in one period, we provide an explicit algorithm for constructing these approximating sets and include an analysis of the computational considerations, along with a numerical example. The novelty of our approach is in formulating, in the limit, necessary and sufficient conditions for stability of switched linear systems based solely on the set of admissible switching signals. Our analysis is valid regardless of the eigenvalues of the system matrices.

Keywords:

Circuits and systems

Filtering

Filters

Switching systems

Communication systems

Communication networks

Event detection

Radio access networks

Regional area networks

Wireless sensor networks

Switched systems

stability of hybrid systems

linear parameter-varying systems

Approximating Sets of Stabilizing Periodic Switching Signals

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