Estimation of Solution Matrix of Perturbed Continuous Riccati Matrix Equation

The Riccati matrix equation has a theoretical and practical importance in the control theory and the state estimation problems.The estimation of the solution matrix of the perturbed continuous Riccati matrix equation is studied in this paper.The perturbation parameters of this equation are of norm-bounded uncertainty.The new upper and lower bounds of the solution matrix for the perturbed continuous Riccati matrix equation are derived by constructing two semi-definite matrices,using matrix inequalities and characteristics of eigenvalues of the matrices.The calculations of upper and lower bounds require only the eigenvalues of the matrices and the solution of linear matrix inequalities.All estimations of bounds are given by matrix inequalities.Thus one does not have to solve the higher-order equation.The results obtained are verified by a numerical example,and the feasibility is illustrated.