I will first discuss a family of orthogonal matrix polynomials $\{P_j(x,\alpha)\}_{j\ge 0}$ defined with respect to the matrix measure $e^{-\alpha x}\,d\sigma(x)$, where $\sigma$ is a monotone nondecreasing $q\times q$ matrix-valued function on $[0,+\infty)$ and $\alpha\ge 0$ is a parameter. These polynomials satisfy a matrix three-term recurrence relation whose coefficients $A_j(\alpha)$ and $B_j(\alpha)$ evolve according to the matrix Toda equations. In the second part of the talk, I will explain how a suitable polynomial $P_n(x,\alpha)$ from this family can be used to construct an explicit bounded positional control $u(x)$ for the linear system \[ \dot{x}=Ax+Bu,\qquad \|u\|\le d. \] This control law incorporates the polynomial $P_n$ directly and guarantees finite-time stabilization: for any initial state $x^0$ belonging to a neighborhood of the origin, the resulting trajectory $x(t,x^0)$ reaches the origin in a finite time $T=T(x^0)$.