In this note we prove that, for analytic systems satisfying the strong accessibility rank condition, generic inputs produce trajectories along which the linearized system is controllable. Applications to the steering of systems without drift are briefly mentioned.

We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N -component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is based on reducing to a special nonlinear...

If A is a nonsingular M -matrix, some new upper and lower bounds on the minimum eigenvalue τ(A) of A are given. These bounds improve some results of Tian and Huang and are more accurate than Li et al. in some cases. In addition, we obtain some new bounds on the minimum eigenvalue of a nonsingular M -matrix A , which can give affirmative conclusions about whether bounds for the minimum eigenvalu...

In this work we consider the concept of differential flatness defined by Fliess, Levine, Martin and Rouchon. The structural property of k-flatness (the case in which flat outputs depends up to the kth derivative of the inputs) is studied based on the properties of the dynamic extension algorithm and the Cartan-Kähler theorems on the existence of integral manifolds of exterior differential syste...

The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of th...

The novel concept of a cyclic sequence of a digraph that has precisely one factor is defined, and is used to characterize the entries of the inverse of a matrix with such a digraph. This leads to a characterization of a strongly sign-nonsingular matrix in terms of cyclic sequences. Nonsingular nearly reducible matrices are a well-known class of matrices having precisely one nonzero diagonal, an...

A ray–nonsingular matrix is a square complex matrix, A, such that each complex matrix whose entries have the same arguments as the corresponding entries of A is nonsingular. Extremal properties of ray– nonsingular matrices are studied in this paper. Combinatorial and probabilistic arguments are used to prove that if the order of a ray– nonsingular matrix is at least 6, then it must contain a ze...