On dual algebraic Riccati equations

Abstract

Dynamic programming complexity and application," in hoc. 27th IEEE Cod. Decision Contr., vol. 2, pp. 1551-1558, Dec. 1988. Allaint, FXIFORTRAN Programmer's Handbook. Acton, MA: Alliant Computer Systems Corporation, 1985.G. M. Amdahl, "Validity of the single processor approach to achieving large scale computing capabilities," Computer Design, vol. 6, M. Athans, "The role and use of the stochastic linearquadratc-Gaussian problem in control system design," IEEE Tram. Automat. "Implementation of linear algebra algorithms of dense matri m on a vector pipeline machine," SIAM J. Rev., vol. 26, pp. 91-112, Jan. 1984.J. Douglas, Jr. and T. W o n t , "Galerkin methods for parabolic Throughout the note, we shall assume H has no eigenvalues on the imaginary axis. Then the four solutions to the dual algebraic Riccati equations can be found as follows:Step 1: Compute a reordered real Schur decomposition of the Hamiltonian matrix H, i.e., ,=U['-0 s+ ' ] U T

The Riccati Equation

“…Another efficient algorithmicapproach to dual Riccati equations can be found in[227]. Then: 1. there exists a unique symmetric stabilizing solution to (*) if and only if M has no pure imaginary eigenvalues and rank ( Z:~ I) = n 2. there exists a unique symmetric anti-stabilizing solution to (*) if and only if M has no pure imaginary eigenvalues and ( Z12 ) rank Z22 _ I = n .…”

Global compact passive macromodeling algorithms for high-speed circuits

“…The proposed algorithm is based on passive truncated balance realization (TBR). In order to reduce the com putational cost during second-level reduction using PR-TBR, w e present appropriate application of results from control theory [92] A brief summary of the proposed second-level passive reduction algorithm (FPTBR) for generating compact passive macromodels is given below, in terms of pseudocode.…”