The existing results on the leader-following consensus problem for linear discrete-time multiagent systems over jointly connected switching digraphs only apply to systems without exponentially unstable modes. In this article, we will remove this restriction by employing a more general class of distributed control laws which includes a set of weight coefficients. By introducing the average radius for a switched matrix which is determined by the Laplacian matrix of the switching digraph of the multiagent system and the set of the weight coefficients, we show that the leader-following consensus problem is solvable if the product of this average radius and the spectral radius of the system matrix is less than unity. Since this average radius can be made less than unity by appropriately choosing the weight coefficients, our result applies to systems containing certain exponentially unstable modes. As a byproduct, the upper bound of the convergence rate can also be specified. Moreover, for the case where the switching digraph is acyclic jointly connected, we prove that the average radius can be made zero by a set of weight coefficients, and, hence, the leader-following consensus can always be achieved regardless of the system mode. Interestingly, the tracking error in this case vanishes in finite time.