Technical communique: An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

Authors:
Amir Shahzad;Bryn Ll. Jones;Eric C. Kerrigan;George A. Constantinides
Affiliations:
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK;The Scottish Association for Marine Science, Scottish Marine Institute, Oban, Argyll PA37 1QA, UK;Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK and Department of Aeronautics, Imperial College London, London SW7 2AZ, UK;Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK
Venue:
Automatica (Journal of IFAC)
Year:
2011

Citing 3
Cited 1

A Perturbation Analysis of the Generalized Sylvester Equation $(AR - LB, DR - LE) = (C, F)$

SIAM Journal on Matrix Analysis and Applications
Solution of the matrix equation AX + XB = C [F4]

Communications of the ACM
On parameter and state estimation for linear differential-algebraic equations

Automatica (Journal of IFAC)

Solvability conditions and general solution for mixed Sylvester equations

Automatica (Journal of IFAC)

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Abstract

Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained by exploiting the structure of the involved matrices. The proposed algorithm removes the need to solve a standard Sylvester equation or to invert a matrix. The improved performance of this new method over existing techniques is demonstrated by comparing the number of floating-point operations and via numerical examples.