Using the differential-geometric control theory, we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to, via a change of coordinates and restricted smooth state feedback, a generalized normal form called —normal form, which includes Brunovsky canonical form and feedback linearizable systems in a lower-triangular form as its sp...

For a set of integers A, we consider \(R(A)=\{a/b: a, b\in b\ne 0\}\). It is an open problem to study the denseness R(A) in p-adic numbers when A nonzero values attained by integral form. This has been answered for quadratic forms. Very recently, Antony and Barman have studied this diagonal binary cubic forms \(ax^3+by^3\), where b are integers. In article, We extend their results \(ax^n+by^n\)...