The estimation and existence conditions of the solution for the perturbed continuous time algebraic Lyapunov equation

In this paper, the estimation problem of the solution matrix about the perturbed continuous time algebraic Lyapunov equation (PCTALE) is discussed. The estimation of upper and lower bounds of the solution matrix to the equation under a certain uncertainty assumption are presented by applying the calculation properties of matrix and some inequalities, and the estimation results are given by continuous time algebra Riccati equations(CTARE) or inequalities. At the same time, some existence conditions of symmetric positive definite matrix solution are shown for PCTALE. Finally, the effectiveness of parts of the results is shown by an example.