On the estimation of solutions to perturbed discrete matrix Lvapunov equations

The estimation of the solution to the perturbed discrete matrix Lyapunov equation is studied. The existence condition and upper and lower bounds estimation of the solution to the equation under the structured uncertainty assumption are presented by applying the operational property of matrix and Lyapunov stability theory, the estimation is then determined by a linear matrix inequality (LMI) and two matrix algebra Riccati equations. The concrete form of matrix algebra Riccati equations are also given for some uncertainty assumptions. Finally, the effectiveness of above results is shown by an example.