Maximum principle application to deterministic linear systems optimal control synthesis is considered most fully in the literature.
In linear systems, at present, the problem of choosing the initial value of Ψ0 vector for specified transition in the system
x' = Ax + Bu from x(t0) ∈ M(t0) to x(t1) ∈ M(t1)
remains unsolved. The exact solution of this problem is unknown (and hardly possible) Boltyansky (1969). The article conserns an approach that allows to determine the Ψ0 vector reachability domain, its dynamic interpretation through the eigenvalues of the matrix A, and the duration of the transition process.