On the Existence of Solutions of Matrix Riccati Equation When Hamiltonian Matrix Has Roots on the Imaginary Axis

Abstract

The conditions of existence of a unique, real, symmetric and non-negative definite solution of the matrix Reccati equation is derived when the Hamiltonian matrix composed of coefficient matrices of system equations has eigenvalues on the imaginary axis in the complex plane.
Such conditions are precisely determined based on the concept of the detectability and quasi-stabilizability.
The method established in this paper is useful in deriving stationary solutions of matrix Riccati equations when sinusoidal or constant signals are estimated by mean of Kalman filters.