Perturbation bounds and characterisation of the solution of the associated algebraic Riccati equation Original Research Article

The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and component-wise) and non-linear non-local perturbation bounds are obtained. The conditioning of the AAMRE is determined in particular. A full characterisation of the solution of AAMRE in terms of neutral subspaces of certain Hermitian matrix is given which is a counterpart of the characterisation of the solutions to the standard Riccati equation in terms of the invariant subspaces of the corresponding Hamiltonian matrix. A reliable method to obtain all solutions to AAMRE is briefly outlined.