Analytical design of a linear controller and a multidimensional analog of solid state dynamics equations

A linear finite dimensional stationary control system is described by the pair $(A, B)$ where A is a linear operator in the state space and $B$ is a linear operator of mapping from the control space into the state space. The way to choose a linear operator $K(A,B,D)$ which would map from the state space into the control space while making the operator $F(A,B,D)=A-BK(A,B,D)$ stable is referred to as design of a stanie system where $D$ is an element of a parameter set. With a fixed way to design the linear controller analytically and fixed $B, D$ an operator set $A$ is described which leads to $F(A,B,D)$ having a specified spectrum. This set laminates into invariant tori of a quite integrable Hamiltonian system. Applications of this result are discussed.