A generalization of the matrix sign function solution for algebraic Riccati equations

This paper extends the use of the matrix sign function to the solution of generalized algebraic Riccati equations [4] for both continuous- and discrete-time systems. These problems involve Hamiltonian and symplectic pencils, respectively, rather than the standard Hamiltonian and symplectic matrices [4]. While ih is possible to convert a generalized eigenproblem or pencil N -
₁
L into a standard eigenproblem for L-1N if L is nonsingular, it may be numerically undesirable to do so. The approach outlined in this paper makes explicit computation of L-1N unnecessary and extends use of the matrix sign function to generalized eigenvalue problems.