# What is State space: Definition and 86 Discussions

A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.
For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space.

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1. ### State Space Representation of a 1D Point Mass Floating in Space and Actuated by Two Lateral Thrusters

(u1*T1) + (u2*T2) = m (x dot dot), [1.1] where (x dot dot) is the 2nd derivative of the point-mass position with respect to time, u1 is the control input for the 1st thruster, u2 is the control input for the second thruster. Rearranging equation 1.1 yields (x dot dot) = (T1/m)*u1+...
2. ### I Spectral Decomposition of the State Space

I'm looking to check my understanding of the information below and ultimately get a better understanding of it. Is spectral decomposition a mathematical procedure? Does "the state space of the measured system" refer to the possible values that the system could take, when measured?
3. ### I Vector operator acting on a ket gives a ket out of the state space

Definition of linear operator in quantum mechanics "A linear operator ##A## associates with every ket ##|\psi\rangle \in \mathcal{E}## another ket ##\left|\psi^{'}\right\rangle \in\mathcal{E}##, the correspondence being linear" We also have vector operators ##\hat{A}## (such as a position...
4. ### I Dimensions of quantum cell automata's state space

In the paper C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573 about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...

43. ### Finding a State-Space Representation for Helicopter Pitch Angle Control

I need help finding a state-space representation for the given system and locally linearizing it... Objective is to control the pitch angle theta, as an output, of the helicopter by regulating the rotor angle u, as an input. This is what I've done, but apparently it isn't correct, and I...
44. ### How to Convert Mechanical System Equations to State Space Form?

JL*QL'' + BL*QL' + k(QL - Qm) = 0 Jm*Qm'' + Bm*Qm' - k(QL - Qm) = u This is the equation set I have for a motor with a load. QL'' means second derivative and QL' means first derivative. I need to be able to obtain the state space representation of this model where X = [QL;QL';Qm;Qm'] (This is...
45. ### Is a state space with indistinguishable particles a quotient? Of what?

I’ve been trying to understand how having indistinguishable particles in a system changes the nature of the state space. The QM texts I have gloss over this. A typical approach is to define the symmetric and anti-symmetric kets that serve as a basis for the eigenspace containing...
46. ### Transfer Function to State Space Calculator Program

Hi, Does anyone know a program that I can put on my TI-84 calculator that will allow me to input any transfer function and get the state space representation of the system or the other way around. For example G(s) = \frac{\sum(K_{i}s^{i})}{\sum(P_{i}s^{i})} The calculator prompts you...
47. ### Engineering Transfer Function and State Space Analysis of Op-Amp circuit

Homework Statement http://imagizer.imageshack.us/v2/800x600q90/690/0tab.png I'm asked to find the transfer function and then find the state space representation and seem to be stuck. Homework Equations The Attempt at a Solution My textbook states that for a noninverting...
48. ### Electrical Engineering - State Space - Matlab

Homework Statement \dot{} I'm given the following circuit http://imagizer.imageshack.us/v2/800x600q90/43/bwka.png Homework Equations The Attempt at a Solution I come up with the transfer function to be G(s) = \frac{s}{2+\frac{1}{s}}. The question asks me to Plot step...
49. ### What is the precise mathematical claim in Haag's theorem?

Hi guys! So this question has been bugging me a bit and I can't seem to find any textbook (at least, restricted to physics textbooks) that talks about it. In QM, the overarching formalism is clear. We have ##L^2(\mathbb{R})## and states are given by ##|\psi\rangle \in L^2(\mathbb{R})## such...
50. ### ARMA model/IIR filter in state space

Homework Statement Write an IIR (or ARMA) model in state space representation: Homework Equations y(k) = b_1 y(k-1) + \cdots + b_p y(k-p) + a_0 u(k) + \cdots + a_r u(k-r) The Attempt at a Solution I found much info how to write it in space state representation but no explanation...