The generation of discrete-time Q-Markov covers via the inverse solution of Lyapunov equation

A novel method for generating q-Markov covers for SISO (single-input single-output) discrete-time systems is proposed. It is based on first computing the impulse-response Gramian from the Markov parameters and covariances, and then solving the Lyapunov equation inversely to get the system matrices in controllability canonical form. Given the markov parameters and the covariances, exactly two q-Markov covers can be obtained by solving the Lyapunov equation inversely to get the system matrices. The method is illustrated by a numerical example and is shown to be computationally simple