Solving Algebraic Riccati Equations with SLICOT

The numerical solution of algebraic Riccati equations is a central issue in computer-aided control systems design. It is the key step in many computational methods for model reduction, filtering, and controller design for linear control systems. We discuss recent advances in the solvers for continuous-time and discrete-time algebraic Riccati equations available in the SLICOT Library (Subroutine Library In COntrol Theory) and compare their performance with the corresponding solvers in the Matlab toolboxes. Keywords— algebraic Riccati equations, numerical algorithms, computer-aided control system design, numerical linear algebra, software library

[1]  Peter Benner,et al.  Accelerating Newton's Method for Discrete-Time Algebraic Riccati Equations , 1998 .

[2]  Peter Benner,et al.  DAREX - A Collection of Benchmark Examples for Discrete-Time Algebraic Riccati Equations (Version , 1999 .

[3]  R. Byers.  Solving the algebraic Riccati equation with the matrix sign function , 1987 .

[4]  Jack Dongarra,et al.  LAPACK Users' Guide, 3rd ed. , 1999 .

[5]  Vasile Sima,et al.  Algorithms for Linear-Quadratic Optimization , 2021 .

[6]  Sabine Van Huffel,et al.  SLICOT—A Subroutine Library in Systems and Control Theory , 1999 .

[7]  Peter Benner,et al.  CAREX - A Collection of Benchmark Examples for Continuous-Time Algebraic Riccati Equations (Version , 1999 .

[8]  Wodek Gawronski,et al.  Balanced Control of Flexible Structures , 1995 .

[9]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[10]  S. Van Huffel,et al.  SLICOT and control systems numerical software packages , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[11]  V. Mehrmann,et al.  A new method for computing the stable invariant subspace of a real Hamiltonian matrix , 1997 .

[12]  Peter Benner,et al.  Computational Methods for Linear-Quadratic Optimization , 1999 .

[13]  R. Chiang,et al.  Robust control toolbox , 1996 .

[14]  Peter Benner,et al.  An exact line search method for solving generalized continuous-time algebraic Riccati equations , 1998, IEEE Trans. Autom. Control..

[15]  Jack J. Dongarra,et al.  An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.

[16]  V. Mehrmann.  The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution , 1991 .

[17]  W. Gawronski.  Dynamics and control of structures : a modal approach , 1998 .

[18]  R. Ober.  Balanced parametrization of classes of linear systems , 1991 .

[19]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[20]  Jack J. Dongarra,et al.  Algorithm 679: A set of level 3 basic linear algebra subprograms: model implementation and test programs , 1990, TOMS.

[21]  Michael Green,et al.  Balanced stochastic realizations , 1988 .

[22]  Gary J. Balas,et al.  μ-analysis and synthesis toolbox: for use with Matlab , 1994 .

[23]  Andras Varga,et al.  A MATLAB MEX-file environment of SLICOT , 2002 .

[24]  A. Laub,et al.  On the numerical solution of the discrete-time algebraic Riccati equation , 1980 .

[25]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.

[26]  Biswa Nath Datta,et al.  Linear and numerical linear algebra in control theory: some research problems , 1994 .

[27]  V. Mehrmann,et al.  A MULTISHIFT ALGORITHM FOR THE NUMERICAL SOLUTION OF ALGEBRAIC RICCATI EQUATIONS , 1993 .

[28]  P. Lancaster,et al.  The Algebraic Riccati Equation , 1995 .

[29]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[30]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[31]  Balas,et al.  [ z-analysis and Synthesis Toolbox * ( p-tools ) t , 2002 .

[32]  Andras Varga,et al.  Computation of Normalized Coprime Factorizations of Rational Matrices , 1998 .

[33]  Vasile Sima,et al.  A MATLAB MEX-file environment of SLICOT. SLICOT Working Note SLWN1999-11 , 1999 .

[34]  P. Dooren.  A Generalized Eigenvalue Approach for Solving Riccati Equations , 1980 .