New lower solution bounds of the continuous algebraic Riccati matrix equation

In optimal and robust control problems, the so-called continuous algebraic Riccati equation (CARE) plays an important part. By utilizing some matrix inequalities and linear algebraic techniques, new lower matrix bounds for the solution of the CARE are derived. Following the derived bounds, iterative algorithms are then developed to obtain sharper solution estimates. In comparison to existing results, the obtained bounds are less restrictive. Finally, we give numerical examples to demonstrate the effectiveness of our results.