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# Questions tagged [state-space]

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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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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: $$y_{t} = x_{t} + \varepsilon_{t}\\ x_{t} ... 1answer 109 views ### Continuous time double exponential filtering in state space form? I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem. Typically, this model is expressed as a pair ... 1answer 339 views ### What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form) I'm using reference from here and here. This is Laplace transfer function of DC Control Speed System:$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$Where, \omega is the motor angular ... 0answers 95 views ### Recursive Least Square For Filtering I just started doing research on Recursive Least Square for filtering noises such as sensors and dc motors noises. The only thing I've seen on the internet was Theoretical information about RLS but ... 1answer 11k views ### Why eigen values and poles of a system are equivalent? In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides. When the model is ... 0answers 36 views ### State space representation using a given nilppotent matrix I want to build a question on state space using a given, nilpotent matrix, A.$$q[n+1]=Aq[n]+Bx[n]y[n]=Cq[n]+Dx[n]$$Usually, I am using the canonical form so there is no problem extracting A,... 1answer 29 views ### Offline State Estimation Imagine I have a nonlinear system:$$ \frac{\text{d} x}{\text{d} t} = f(x,t)\\ y = g(x). $$I can design a nonlinear observer to estimate the state x based on the measurements y. However, this ... 0answers 39 views ### Augment State Space Model with Derivative of State Problem How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system$$ \...
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 $T(s)$, ...