| Autor: |
Ofir, Ron, Margaliot, Michael, Levron, Yoash, Slotine, Jean-Jacques |
| Předmět: |
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| Zdroj: |
IEEE Transactions on Automatic Control; Sep2022, Vol. 67 Issue 9, p4994-5001, 8p |
| Abstrakt: |
The flow of an $n$ -dimensional $k$ -contracting system, with $k\in \lbrace 1,\ldots,n\rbrace$ , contracts $k$ -dimensional parallelotopes. For $k=1$ , this reduces to a standard contracting system. One reason for the usefulness of 1-contracting systems is that many interconnections of contracting subsystems yield an overall 1-contracting system. Here, we derive a new sufficient condition guaranteeing that the system obtained from the series interconnection of two subsystems is $k$ -contracting. This is based on a new formula for the $k$ th multiplicative and additive compounds of a block-diagonal matrix (BDM), which may be of independent interest. As an application, we find conditions guaranteeing that 2-contracting systems with an exponentially decaying input retain the well-ordered behavior of time-invariant 2-contracting systems. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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