# Questions tagged [state-space]

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### Got stack in calculating state-space representation

I got stack in the process of deriving a state-space representation of the following system: There is an electrical oven described as follows: control of the power supply $u$, heating efficiency ...
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### Is there any difference in Implementing sigma delta modulator using filters and state space model in FPGA?

Sigma delta modulation is extensively used in quantization to reduce quantization noise. In the literature one can see different architecture for example python-deltasigma to implement a modulator. ...
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### Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): \begin{align} X_{t+1}&=FX_t + V_t\\ Y&=HX_t+W_t\\ V_t &\sim \mathcal N(0,Q)\\ W_t &\sim \...
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### Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
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### 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 ...
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### Is this model nonlinear?

I have this state-space model: Is this state space model nonlinear? If it is, why is that?
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### How to form Kalman filtering matrices for a problem with variable acceleration?

Assuming we have time vector $T$ with constant time step $dt$ position vector $X$ velocity vector $V$ acceleration vector $A$ All vectors $X, V, A$ have noise on their measurement ( $n_x$ , $n_v$ , ...
I'm trying to change this filter transfer function to state space representation $y_t=\frac{1+b_1 z^{-1}}{1+a_1 z^{-1} +a_2 z^{-2}}u_t$ I tried writing it as time series $y_t+a_1 y_{t-1}+... 1answer 751 views ### The two types of stability and “Why exponential” When I was learning about LTI systems, I noticed that LTI system is said to be BIBO stable if and only if its square sum of impulse response is finite. This expression is found on many textbook of ... 1answer 159 views ### Doubt in state space representation$y$is scalar observations and so C will be a 1x2 matrix. I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations$y$... 3answers 7k views ### When Is a Kalman Filter Different from a Moving Average? this thread asks when a discrete time Kalman filter is better/different from a simple moving average of the observations: Why use a Kalman filter instead of keeping a running average? there's no ... 1answer 1k views ### kalman filter with time-varying noise? in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations:$x(t+1) = Ax + wy(t) = Cx(t) + v$... 2answers 610 views ### How to intuitively understand the state space formulation of discrete time system? The SS formulation of DT system is given by $$x[(k+1)T] = Ax(kT) + Bu(kT)$$ $$y(kT) = Cx(kT) + Du(kT)$$ Note: T is the sampling period and often omited Can someone explain to me why the state ... 2answers 107 views ### How to find the output signal of a filter using state space matrices? I have a filter. It has two poles and two zeros. I found the state space equations and the matrices A, B, C, and D Now. I have 9 samples that I need to process with my filter. How do I use A,B,C,D ... 2answers 689 views ### Does the system matrix being singular tell us anything about the system? If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system? 2answers 2k views ### Why is my discretized transfer function unstable when my discretized state-space model is stable? I am working with a 30-state, 14-input linear model that is described by a state-space model: model_state_space = ss(A, B, C, D); The model is extremely slow (it ... 2answers 163 views ### How to find derivative of 2-D elliptical Gaussian function with different standard deviations along$x$and$y$directions? I am trying to find the 2-D derivative of an elongated Gaussian density. The Gaussian has standard deviations$\sigma_x$and$\sigma_y$. How can I get the scale-normalized 2-D Gaussian derivative in ... 1answer 1k views ### state space formulation of a sinusoidal system Let$f=A\sin{\omega t}=x_1$and$\dot{f}=A\omega\cos{\omega t}=\dot{x}_1=x_2$. Let the output be$y=cA\omega$, where$c=1$is a constant. I want to represent this in a state space formulation:$\dot{...
The code in this page solves the Least Squares problem for the following dynamic model: $\dot{y}=ay+bu$ where $a$ and $b$ are constants, $u$ is an input. The code is as follow: ...