Nonsmooth Analysis in Systems and Control Theory

Generalized gradients and subgradients These terms refer to various setvalued replacements for the usual derivative which are used in developing differential calculus for functions which are not differentiable in the classical sense. The subject itself is known as nonsmooth analysis. One of the best-known theories of this type is that of generalized gradients. Another basic construct is the subgradient, of which there are several variants. The approach also features generalized tangent and normal vectors which apply to sets which are not classical manifolds. A short summary of the essential definitions is given in §III.