Modeling with Nonsmooth Dynamics by Mike R. Jeffrey

Author:Mike R. Jeffrey
Language: eng
Format: epub
ISBN: 9783030359874
Publisher: Springer International Publishing

We then write the following.

Definition 5.4

The nonlinear switching system corresponding to (5.1) is given by

(5.8)

where F depends smoothly on x and on switching multipliers ν j as defined in (5.7b). Solutions of (5.8) will be called nonlinear solutions of (5.1).

The correspondence required in Definition 5.3 can be achieved by associating each i ∈ Z N with a binary string i 1…i m of 0s and 1s, by either

(5.9)

where (a) simply numbers regions so , while (b) identifies i as the binary string i = i 1i 2…i m itself.

The simplest example of a canopy is then given by writing

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