The class of robust stability problems considered involves structured, repeated, linear time-varying, induced ∞-norm bounded perturbations. A well known sufficient condition for these robust problems follows from the scaled small gain theorem and is stated in the form of a scaled 1-norm minimization problem with block diagonal scaling matrices. A procedure reducing the domain in the search for ...

In kernel–based methods, how to handle the scaling or the choice of the shape parameter is a well– documented but still an open problem. The shape or scale parameter can be tuned by the user according to the applications, and it plays a crucial role both for the accuracy of the method and its stability. In [7], the Variably Scaled Kernels (VSKs) were introduced. The idea is to vary the scale in...

We study noncommutative (NC) field theory of a real NC tachyon and NC U(1) gauge field, describing the dynamics of an unstable Dp-brane. For every given set of diagonal component of open string metric G0, NC parameter θ0, and interpolating electric field Ê, we find all possible static NC kinks as exact solutions, in spite of complicated NC terms, which are classified by an array of NC kink-anti...