driccond (Robust Control Toolbox)

Robust Control Toolbox

driccond

Condition numbers of discrete algebraic Riccati equation.

Syntax

```
[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

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