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. jegues

    Understanding State Space Representation for First-Order Dynamic Systems

    Homework Statement A first-order dynamic system is represented by the differential equation, 5\frac{dx(t)}{dt} + x(t) = u(t). Find the corresponding transfer function and state space reprsentation. Homework Equations The Attempt at a Solution Putting the equation in the...
  2. Y

    State space of QFT, CCR and quantization, and the spectrum of a field?

    State space of QFT,CCR and quantization,spectrum of a field operator? In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): [ϕ(x),π(y)]=iδ(x−y) ------ (1) in analogy with the ordinary QM commutation relation...
  3. N

    Reference Input for State Space Controller

    In the design of a State Space controller using state feedback the input to the plant is given as (where y=x & D=0): u=-Kx If there is a "reference input" then it would be: u=-Kx+r So the state feedback without the reference input simply drives all of the state variables to zero. When there is...
  4. C

    State space representations for different system configurations

    Homework Statement Homework Equations This is the problem that I am trying to solve. The Attempt at a Solution https://docs.google.com/file/d/0B0Wxm870SWTNV0xjdmVRc09TTm8/edit The approach of solving this problem is to first convert the two systems' state space...
  5. A

    Higher order DE to State space

    Hey, I've been trying to run a few simulations in Matlab using ODE45. This algorithm requires a function which gives the first order differential as an output i.e a state space format (Correct me if I'm wrong here). If its a normal N order differential such as d2x/dt2 + dx/dt -1 =0 . dx/dt...
  6. M

    Engineering Find the state space solution for a circuit

    Homework Statement Find the state space solution, the output is Vo Homework Equations VL = L*di/dt IC = 1/C*(integral of current) KCL KVL The Attempt at a Solution I tried to apply KCL and KVL but still can't figure it out. This one has been driving me nuts for 4 days.
  7. J

    The dimensionality of the state space of a quantum system

    Hi, I haven't posted for a while. I've seen this topic come up a few times, but it always seems to me that a few points aren't made clear. Can I just check the following is true? 1) The state space of a quantum system is always an infinite-dimensional seperable Hilbert space i.e. a Hilbert...
  8. S

    State space modeling of parallel capacitors

    Hi there, I have been thinking about how to actually describe a system input filter consisting of several caps and an inductance in the state-space representation. The topology follows: a DC source to inductor to two parallel caps that are referenced to the same potential as the voltage...
  9. N

    The state space in quantum field theory

    I'm a grad student in math, and I've been trying to learn some physics on the side by taking some classes and reading books. I took a class on quantum field theory last semester that was taught out of Srednicki; the class was very good, but I found myself at the end with a conceptual question...
  10. L

    Obtaining state space from transfer functions

    1. The problem statement I have a MIMO system with two inputs and two outputs. I have all transfer functions between inputs and outputs. I want to obtain a state space model that describes this system. All transfer functions are of 3rd degree. Homework Equations "Transfer matrix": HP(s)=[H11...
  11. C

    State Space control dervatives of input in B matrix.

    Hi guys, I am trying to put a series of differential equations into sate space form. The problem that I have come up against is that I end up with a differential in my B term (control matrix) and I am unsure of how to deal with this. Is there an easy way of doing this? Does anyone have any...
  12. P

    State Space Analyis - the 'B' matrix

    Below is a screen shot from state space analysis in "Control Engineering" by Ogata. http://www.flickr.com/photos/66943862@N06/6230432028/" I am trying to get at 3-20 from 3-18. Can't the u part of the matrix also be written as [1/m 0]T instead of [0 1/m]T? What's the rationale in choosing...
  13. A

    Writing Output in State Space Form: RLC Circuit Example

    the general form of state space output is y=cx+du which means that output is linear combination of state variables and inputs my question is can we write output in this form when our output is not combination of state variable for example in rlc circuit state variables are vc and IL now if we...
  14. M

    State space and its subspace : finding a basis

    Hello. I really need help with this one: Homework Statement I have a 3 dimensional state space H and its subspace H1 which is spanned with |Psi> = a x1 + b x2 + c x3 and |Psi'> = d x1 + e x2 + f x3 Those two "rays" are linearly independent and x1, x2, and x3 is an...
  15. R

    State space representations in LTI systems

    I just started my first graduate level controls class this semester, and it looks like my professors notes aren't going to be quite enough. Can anybody recommend a good book with lots of state space representation examples, or if not a book, a website would do fine as well. Thanks for any help.
  16. K

    Control Systems, State space to Transfer Function

    Hi guys, Need a little help with an example my tutor and I are trying to work through. We're converting a dynamics system from a state space representation to a transfer function. This is where we are at so far... [s^2 + (C/Mb)S + (K1/Mb), -((C)S + K1)/Mb; -((C)S + K1)/Mw, S^2 +...
  17. Rasalhague

    State space, beginner's question

    Background. I recently started reading A Quantum Mechanics Primer by Daniel T. Gillespie. I'm up to the section on Banach spaces in Kreyszig's Introductory to Functional Analysis with Applications, and have looked ahead to the chapter on applications to quantum mechanics, Ch. 11. I've also read...
  18. S

    State Space Form of Projectile EOM with Air Resistance

    I have equations of motion for a projectile with air resistance: where q = [x; y] m \ddot{q_1} = -k \dot{q_1} m \ddot{q_2} = -k \dot{q_2} - mg I need to convert it into state space form, with the state X = [q; \dot{q}]. I'm told state-space form is a first order vector ODE: \dot{X} = [\dot{q}...
  19. D

    State Space What does u(.) mean

    I am trying to understand what is meant by u(.) in control systems, specifically in regards to state space representation. To give context, " Find a control law u(.) which steers the state of" then a the A and B matrices are given (0; 0) to (1; 0) in one unit of time. I don't need help solving...
  20. E

    Uncontrollable States in State Space

    Hi Guys/Gals If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix...
  21. D

    Controllability of state space equation

    Homework Statement I have calculated the following mechanical system \left( \begin{array}{c}\dot{\mathbf{x_1}}(t) & \dot{\mathbf{x_2}}(t) \end{array} \right) = \left( \begin{array}{cc}-0.5 & 0 & 0 & -1\end{array} \right) \cdot \left( \begin{array}{c}x_{1}(t) & x_{2}(t)\end{array}...
  22. C

    Use of state space equations to model a dynamic system

    Hello, I enclose a jpeg of the circuit and two simulink jpeg files. The first mdl file - First Test circuit sucessfully models the circuit. The second one where I attempt to model the circuit from its state space equation does not. Can anyone help me to create a correct state space model...
  23. F

    MATLAB Finding Damped Frequency of a State Space Matrix Equation with MATLAB

    Matlab, how to find damped frequency of a sate space matrix euqation? Hello: I am working on a tyre mechanic problem basically it just a vibration problem so far I have dervied the the state space equation which is in the form x'=[A]x+[B]u [A] is 2x2 matrix, [B] is a 1X2 matrix (u...
  24. K

    How to convert transfer function to state space

    Hi,how can i convert the following transfer function to state space form by hand. H(s)=(s^2+27s+50)/(2s^2+27s+50) Any help will be appreciated!
  25. N

    Multivariable state space where forcing function has derivative terms

    Homework Statement Hi, I have two linear differential equations describing some multivariable dynamic system, and I need to represent the system in a state space representation. This would be normally very easy if the forcing functions on the RHS did not contain derivative terms e.g...
  26. N

    Discrete time state space model: solving for input

    Preface: This homework assignment was due long ago. At this point I am only trying to understand the problem (or really if the posted solution follows the problem) before my exam. I have no real indication that this problem (or even one like it) will be on my final, but I feel that my inability...
  27. M

    Control theory: Laplace versus state space representation

    I'm taking a course in control theory, and have been wondering for a while what the benefits are when you describe a system based on the Laplace method with transfer functions, compared to when you use the state space representation method. In particular, when using the Laplace method you are...
  28. C

    Nonlinear differential equation to state space form

    Homework Statement The problem gives a nonlinear differential equation for a metallic ball suspended under maggnetic levitation: y**(t)=9.81- (0.981u(t))/(y+1)2 (note: y**= second derivative of y)\ where y(t) is the position of the ball and u(t) is the voltage applied ti the magnet...
  29. R

    Transfer function to state space manually

    Hi, how can i convert a transfer function to state space form by hand: e.g.; G=10/(s+10) ??
  30. K

    State Space Differential Equation HW

    Hi I have a problem I need to solve for a class soon. The prof gave a us a homework problem where he gives us a state space representation for one system and connect it in cascade to another system and need the equivalent state space parameters: I'm pretty confused. Heres the question...
  31. K

    Solve State Space Model HW: Find A, B, C, q

    Hi I have a problem I need to solve for a class soon. The prof gave a us a homework problem where he gives us a state space representation for one system and connect it in cascade to another system and need the equivalent state space parameters: Heres the question: x(t)----> |system1 | -->...
  32. A

    Genral state space model - runge kutte

    Hi, Really glad to have found this site... I was hoping someone could help me - have been trying to decipher how to find a way to solve general n order state space model - I started off with RK4 and now I want to expand that but I can't get my head wrapped around the butcher tableau to...
  33. F

    Dimensions of the logistic map state space and quantum chaos.

    Apologies if this is the wrong forum, but I have a pair of thematically connected questions that I can't really fit anywhere else. Please move if this is better suited to the quantum physics forums. My first question being: The Poincare-Bendixon theorem states that chaos can only occur for...
  34. C

    Rough Description of State Space

    I have done only a small bit of reading/studying of quantum mechanics. So, from what I have gathered thus far, I have the following rough semi-graphical description of state space: Imagine a space in which you have a lot, but a definite number of discrete points. Each of those points (state...
  35. J

    State space system model derivation - hard and really fast - PLEASE

    State space system model derivation - hard and really need help fast - PLEASE! Hi, Just found this site (a little too late I fear!). I have an assignment due tomorrow and I can not solve the last part of it. We are able to source information from anywhere to complete the assignment and you...
  36. J

    State space system model - hard and really fast - PLEASE

    State space system model - hard and really need help fast - PLEASE! Hi, Just found this site (a little too late I fear!). I have an assignment due tomorrow and I can not solve the last part of it. We are able to source information from anywhere to complete the assignment and you guys are my...
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