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?
I suggest you to follow https://www.mathworks.com/help/control/ref/ss.html
I know the command.
Is Forward Euler discretization possible with that command from continuous to discrete? Is this method of discretizing possible with the ss command. Furthermore, if I go from discrete to continuous, the system matrices changes in size (A,B,C), which I don't want. Why is this the case? Is this due to the Warning: The model order was increased to handle real negative poles? I used the lines sysd = ss(a,b,c,[],Ts); sysc = d2c(sysd);
However, I want to apply it directly to the discrete model.
Instead of going from discrete to continuous to again discrete.
Here is a classical proven method in discrete time signal analysis: fractional times insertion with associated signal value.
Assume you have discrete sequence of times t(n), t(n+1) with corresponding signal x(t(n)), x(t(n+1)). You define a t(n+1/2) between t(n) and t(n+1) and associated value interpolated.
Fractional pitch prediction for speech coding used this (look in past literature).
You also have literature on signal oversampling in the audio music field, with different sampling rates 8kHz, 32kHz, 48 kHz and 44.1kHz (CD for WAV or PCM)
Renaud Di Francesco
Do you know how that method works for a discrete-time state-space model?
Aparna Sathya Murthy
zpkdata() returns the poles and zeros of the system.
I don't understand what this information could be used for scaling the time of a discrete-time state-space model.
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