We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the original one while allowing to construct the sl...

Let a, b, c, d be elements in a unital associative ring R. In this note, we generalize Cline?s formula for some new generalized inverses such as strong Drazin inverse, Hirano inverse and to the case when acd = dbd dba aca. As particular case, recent results are recovered.

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...