Canonical form for the matrices of linear discrete-time systems

Some applications of canonical matrices to linear continuous-time systems are reviewed. A canonical form is proposed for real nonderogatory convergent matrices, such as the A matrices which occur in the description of linear discrete-time dynamical systems by vector-matrix difference equations of the form xk+1 = Axk + Buk. The new canonical form is applied to the generation of particular and general solutions of the matrix equation ATLA − L = −K, which occurs in the application of Lyapunov theory to the analysis and design of such systems.