# Questions tagged [state-space]

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### How does sampling jitter affect state estimation?

Suppose I have some process which is governed by: $$\vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$ where $u_k$ is the input, and $w_k$ is process disturbance. This process is continuous time in ...
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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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### Simulate butterworth filter with initial condition of state vector in R

I'm working in R with the packages signal and control (don't know wether these are even the best for my use case). I have a high ...
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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: x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
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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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### 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 u1 and u2 are inputs and y1 and y2 are the outputs of the system I tried to place state variables on the ...
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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 ...
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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 ...
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The question might be very simple, but I get a strange result from Kalman Filter. Let us consider the simplest state-space model, the random walk plus noise: $$y_{t} = x_{t} + \varepsilon_{t}\\ x_{t} ... 1answer 390 views ### What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form) I'm using reference from here and here. This is Laplace transfer function of DC Control Speed System:$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$Where, \omega is the motor angular ... 0answers 196 views ### Recursive Least Square For Filtering I just started doing research on Recursive Least Square for filtering noises such as sensors and dc motors noises. The only thing I've seen on the internet was Theoretical information about RLS but ... 1answer 14k views ### Why eigen values and poles of a system are equivalent? In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides. When the model is ... 0answers 37 views ### State space representation using a given nilppotent matrix I want to build a question on state space using a given, nilpotent matrix, A.$$q[n+1]=Aq[n]+Bx[n]y[n]=Cq[n]+Dx[n]$$Usually, I am using the canonical form so there is no problem extracting A,... 1answer 58 views ### Offline State Estimation Imagine I have a nonlinear system:$$ \frac{\text{d} x}{\text{d} t} = f(x,t)\\ y = g(x). $$I can design a nonlinear observer to estimate the state x based on the measurements y. However, this ... 0answers 43 views ### Augment State Space Model with Derivative of State Problem How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system$$ \...
Let $T(s)$ be a transfer function that describes a mechanical system, where the input is force and the output is position. And let $[A,B,C,D]$ be the equivalent state-space representation of $T(s)$, ...