# Questions tagged [state-space]

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### Direct and numerically robust conversion from zero-pole to state-space representation

Note: this question was initially asked in a different community. Encouraged by the comments, I decided to cross-post here too. Given (z,p,k) my goal is to convert to a state-space representation (A, ...
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### Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses?

Let $$\dot{x} = Ax+Bu$$ $$y = Cx + Du$$ be a linear ODE with $x(0)=0$. Here, I am assume $A$ is invertible. As you can see, the relation $$H:u(.) \mapsto y(.),$$ where $(u(.),y(.))$ is a solution to ...
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### Initial conditions of state-space realization

In a discrete-time difference equation (ARX model), the output $y[k]$ is dependent on its past values and inputs, expressed as: $y[k] = -a_1 y[k-1] - ... - a_N y[k-N] + b_1 u[k-1] + ... + b_M u[k-M]$, ...
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### How is the transfer function of a state space representation computed in practice?

I know that if you have a linear time invariant system defined by $$\dot{X} = AX+BU$$ $$Y = CX$$ by "Laplacing" the previous equations, you get the following transfer function in the ...
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### Mismatch between the frequency response of a transfer function and bode plot

I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)): <...
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### How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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### State-space model and/or TF for a $K$-th order linear system given the signal sequence

The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential: \begin{equation} x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
1 vote
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### How to get state-space equations form from a block diagram?

This is the block diagram that I'd like to transform into a state-space representation, where $u_{1}$ and $u_{2}$ are inputs and $y_{1}$ and $y_{2}$ are the outputs of the system I tried to place ...
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### Methods for time series estimation in time domain

I am trying to estimate the clean form of a time series, $u(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is: $$y(t) = u(t) + w(t)$$ My first ...
1 vote
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### States transformation of the bilinear transform

I have used the bilinear (or tustin) transform for a while, have been though the derivation of it and also through the concept of frequency warping. Something that I still not understand that is ...
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### What does it mean for a transfer function to have multiple sets of zeros in the numerator?

I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
1 vote
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### Recursive Least Square For Filtering

I just started doing research on Recursive Least Square for filtering noises such as sensors and dc motors noises. The only thing I've seen on the internet was Theoretical information about RLS but ...