CLOSED-FORM SOLUTION OF THE CONTINUOUS-TIME LYAPUNOV MATRIX EQUATION

A simple algorithm is proposed for a closed-form solution to the conti nuous-time Lyapunov matrix equation using the Routh array, which is us eful for the computation of controllability, observability and cross-G ramians for both SISO and MIMO systems. The proposed algorithm provide s the Gramians directly from the Routh array and thus is more efficien t than existing algorithms. The closed-form solutions can be obtained even for unstable nonminimal systems, provided that all the leading co efficients of the Routh array are nonzero. Numerical examples are incl uded to demonstrate the computational procedure.