Periodic Lyapunov equations: some applications and new algorithms. (English) Zbl 0873.93057

The author’s model is \[ x_{k+1}= A_{k+1}x_k+ B_ku_k,\quad y_k= C_kx_k+D_ku_k, \] where the matrices are periodic. The problems solved by the author are: optimal state feedback periodic control, state feedback stabilization of periodic systems, optimal output feedback periodic control, square-root balancing of periodic systems, solution of indefinite reverse-time discrete periodic Lyapunov equation, solution of low-order discrete periodic Sylvester equations (incl. rouding errors and estimation of condition number), and solution of nonnegative discrete periodic Lyapunov equations. Six algorithms are presented. A set of LAPACK-based Fortran routines have been implemented.


93C55 Discrete-time control/observation systems
93B40 Computational methods in systems theory (MSC2010)
93C57 Sampled-data control/observation systems


mctoolbox; LAPACK
Full Text: DOI