New lower matrix bounds for the solution of the continuous algebraic lyapunov equation

New lower matrix bounds are derived for the solution of the continuous algebraic Lyapunov equation (CALE). Following each bound derivation, an iterative algorithm is proposed to derive tighter matrix bounds. In comparison to existing results, the presented results are more concise and are always valid when the CALE has a non-negative definite solution. We finally give numerical examples to show the effectiveness of the derived bounds and make comparisons with existing results.