ON THE SOLUTION OF THE QUASI RICCATI AND LYAPUNOV EQUATIONS

The classical Riccati equation arises in optimal linear estimation where the state and measurement noise covariance matrices are non-negative definite. The quasi Riccati equation is defined preserving the form of the classical Riccati equation and using noise matrices that are not necessarily non-negative definite. The classical Lyapunov equation results from the classical Riccati equation in the infinite measurement noise case. The quasi Lyapunov equation is defined preserving the form of the classical Lyapunov equation and using complex transition matrix. A method for computing the solution of the quasi Riccati and Lyapunov equations is proposed. The method is based on the algebraic solution of the discrete time Riccati equation, where the eigenvalues of the resultant symplectic matrix are allowed to lie on the unit circle.