Differential Equations with Discontinuous Righthand Sides
Citations
11,085 citations
3,894 citations
Cites background from "Differential Equations with Discont..."
...Discontinuous dynamics, besides making a rigorous analysis difficult (see [9]), may also lead to chattering [10] or excite high frequency dynamics in applications involving flexible structures....
[...]
2,954 citations
Cites background or methods from "Differential Equations with Discont..."
...Filippov (1988) any discontinuous differential equation _ x x ¼ vðxÞ, where x 2 Rn and v is a locally bounded...
[...]
...Let us recall first that according to the definition by Filippov (1988) any discontinuous differential equation _x ¼ vðxÞ, where x 2 Rn and v is a locally bounded measurable vector function, is replaced by an equivalent differential inclusion _x 2 VðxÞ....
[...]
...They are based on results by Filippov (1988)....
[...]
...They are based on results by Filippov (1988) ....
[...]
...Let now "M > 0. As follows from the continuous dependence of the solutions of a differential inclusion on the right-hand side ( Filippov 1988 ) with sufficiently small "M all trajectories concentrate within a finite time in a small vicinity of the origin....
[...]
2,884 citations
2,714 citations