A link is established between the definition of Filippov’s solution concept for ordinary differential equations with a discontinuous right- hand side [A. F. Filippov
, Mat. Sb., N. Ser. 51(93), 99-128 (1960; Zbl 0138.322
)] and Clarke’s generalized gradient [F. H. Clarke
, Optimization and nonsmooth analysis (1983; Zbl 0582.49001
)]. According to Filippov’s definition, solutions to
are those to the differential inclusion
, where K(f) is a suitably defined multifunction depending on f. The authors remark that if f is locally Lipschitz, then
denotes Clarke’s generalized gradient. This relation is useful for computing K in various situations. Such a calculus is applied to the variable structure control of a robot manipulator.