On the Lyapunov matrix equation
Eliezer Y. Shapiro · IEEE Transactions on Automatic Control · 1974
Given the Lyapunov matrix equationA'Q + QA = -Pa fundamental inequality which is satisfied by the extremal eigenvalues of the matricesQandP, providedAis a stability matrix, is established. This result, besides being interesting from a theoretical standpoint, is extremely useful in the determination of suboptimal controllers for the minimum time problem [1].