# American Institute of Mathematical Sciences

March  2019, 9(1): 159-174. doi: 10.3934/mcrf.2019009

## Randomized algorithms for stabilizing switching signals

 1 Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India 2 Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India 3 Systems & Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

* Corresponding author

Received  June 2017 Revised  July 2018 Published  September 2018

Qualitative behaviour of switched systems has attracted considerable research attention in the recent past. In this article we study 'how likely' is it for a family of systems to admit stabilizing switching signals. A weighted digraph is associated to a switched system in a natural fashion, and the switching signal is expressed as an infinite walk on this digraph. We provide a linear time probabilistic algorithm to find cycles on this digraph that have a desirable property (we call it "contractivity"), and under mild statistical hypotheses on the connectivity and weights of the digraph, demonstrate that there exist uncountably many stabilizing switching signals derived from such cycles. Our algorithm does not require the vertex and edge weights to be stored in memory prior to its application, has a learning/exploratory character, and naturally fits very large scale systems.

Citation: Niranjan Balachandran, Atreyee Kundu, Debasish Chatterjee. Randomized algorithms for stabilizing switching signals. Mathematical Control & Related Fields, 2019, 9 (1) : 159-174. doi: 10.3934/mcrf.2019009
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##### References:
Plot for the empirical probability of a cycle being contractive against its length $n$ with $\displaystyle{\Phi (r) = \frac{1}{10}\sqrt{r}}$
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