driccond (Robust Control Toolbox)

Condition numbers of discrete algebraic Riccati equation.

[tot] = driccond(a,b,q,r,p1,p2)

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

tot= [norA,norQ,norRc,conR,conP1,conBey,res]'

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 A_cl = (I_n + 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.

des2ss dsigma, sigma