论文信息 - Efficient and reliable algorithms for condition estimation of Lyapunov and Riccati equations

Efficient and reliable algorithms for condition estimation of Lyapunov and Riccati equations

Efficient and reliable condition estimators for continuoustime or discrete-time matrix Lyapunov and Riccati equations are discussed. The basic calculation for obtaining these estimates is the evaluation of the 1-norm of the inverse of a Lyapunov operator. This is performed by evaluating this operator and its dual on suitably selected values, or, equivalently, by solving related Lyapunov equations. Various strategies for exploiting the symmetric structure of the problem are investigated and compared. The results show that the proposed strategies are highly accurate and very fast.

Sabine Van Huffel | Vasile Sima

[1] S. Hammarling. Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation , 1982 .

[2] Nicholas J. Higham,et al. FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation , 1988, TOMS.

[3] Mihail M. Konstantinov,et al. Computational methods for linear control systems , 1991 .

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

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

[6] A. Barraud. A numerical algorithm to solve AT X A - X = Q , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[7] R. Byers. A LINPACK-style condition estimator for the equation AX-XB^{T} = C , 1984 .

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

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

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