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driccond    See Also

Condition numbers of discrete algebraic Riccati equation.

Syntax

Description

driccond provides the condition numbers of discrete Riccati equation

where P = P2/P1 is the positive definite solution of ARE, and [P2; P1] spans the stable eigenspace of the Hamiltonian

where S = BR-1BT.

Several measurements are provided:

   1
Frobenius norm of matrices A, Q, and BR-1BT (norA, norQ, norRc).
   2
condition number of R (conR).
   3
condition number of P1 (conP1).
   4
Byers' condition number (conBey) [1].
   5
residual of Riccati equation (res).
The output variable tot puts the above measurements in a column vector

For an ill-conditioned problem, one or more of the above measurements could become large. Together, they should give a general information of the Riccati problem.m

Algorithm

Byers' Riccati condition number is computed as [1]

where Acl = (In + SP)-1 A and

See Also

are, aresolv, daresolv, riccond

R. Byers, "Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation," Ph.D. dissertation, Dept. of Comp. Sci., Cornell University, Ithaca, NY, 1983.


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