02 February 2020 5 6K Report

In order to get a better conditioned A matrix, the absolute mean of the eigenvalues of the A matrix should be one (all eigenvalues are between -1 and 1, so within the unit circle and the absolute mean is 0.4389). This could be done by scaling the time.

For the following continuous-time state-space model:

dx/dt = Ax(t) + Bu(t)

y = Cx(t)

the state-space model will look like:

dx/dtau = (1/lambda_avg)*Ax(tau/lambda_avg) + (1/lambda_avg)*Bu(tau/lambda_avg)

y = Cx(tau/lambda_avg)

with

lambda_avg, the absolute mean of the eigenvalues of the A matrix

tau, the new timescale

tau = lambda_avg*t

However, I want to scale the time of a discrete-time state-space model in order to get a better conditioned A matrix:

xi+1|k = Axi|k + Bui|k

yk = Cxk

How could I do that in the same way as for the continuous model?

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