On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations.

In this work, the null controllability problem for a linear system in is considered, where the matrix of a linear operator describing the system is an infinite matrix with on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if ≤- 1, which shows the fine difference between the finite and the infinite-dimensional systems. When ≤- 1 we also show that the system is null controllable in large.

Computing the partition dimension of certain families of Toeplitz graph.

Let = ((), ()) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set () and the edge set (). The distance () between two vertices that belong to the vertex set of is the shortest path between them. A -ordered partition of vertices is defined as β = {β, β, …, β }.

Linear discrete pursuit game with phase constraints.

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints: y∈G, where G is a subset of Rn. We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints.