Reduction of linear discrete dynamic systems to a stationary form by state space extension (Q1280352)

The author treats the linear discrete dynamic system with control and observation \[ x(k+1) = A(k)x(k) + B(k)u(k),\qquad\sigma(k) = H(k)x(k),\tag{1} \] where \(x(k) = x(t_k)\) is the vector state; \(t_k = t_0+Tk\), \(k=0,1,2,\dots\), \(u(k)\) is the discrete control and \(\sigma(k)\) is the measurement vector. The author cites two different transformations so that the matrix \(A(k)\) of system (1) becomes constant. Two theorems on reducibility of system (1) are set out (without proofs).