Abstract
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 - ?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.
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