ON THE SOLUTION OF THE QUASI RICCATI AND LYAPUNOV EQUATIONS
M. ADAM
Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Str., P.O. 35131 Lamia, Greece.
N. ASSIMAKIS
Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, P.O. 35131 Lamia, Greece.
E. FAZAELI
Department of Electrical Engineering, Islamic Azad University, Najafabad Branch, Isfahan, Iran.
G. TZIALLAS *
Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, P.O. 35131 Lamia, Greece.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Riccati equation, Lyapunov equation, algebraic solution