Nonlinear Time-Delay Systems by Claudia Califano & Claude H. Moog

Author:Claudia Califano & Claude H. Moog
Language: eng
Format: epub
ISBN: 9783030720261
Publisher: Springer International Publishing

Since for any , one can check the condition (3.13) step by step, increasing the value of p every step. When for some the condition (3.13) is satisfied, then it is satisfied for all .

Given the set of 1-forms , independent over , the basis of vector space defines the basis for the largest integrable left-submodule contained in .

Lemma 3.2

A set of one-forms is weakly integrable if and only if the left closure of the left-submodule, generated by , is (strongly) integrable.

Proof

Necessity. By definitions of weak integrability and left closure, there exist functions such that , where is the basis of the closure of the left-submodule, generated by . Choose such that for

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