Time-domain state space representation | Wikipedia audio article
Channel: wikipedia tts
Date: 02/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/State-space_representation


00:02:35 1 State variables
00:04:13 2 Linear systems
00:10:41 2.1 Example: continuous-time LTI case
00:14:11 2.2 Controllability
00:14:57 2.3 Observability
00:16:15 2.4 Transfer function
00:23:48 2.5 Canonical realizations
00:30:06 2.6 Proper transfer functions
00:34:13 2.7 Feedback
00:39:07 2.7.1 Example
00:39:25 2.8 Feedback with setpoint (reference) input
00:40:36 2.9 Moving object example
00:46:47 3 Nonlinear systems
00:53:32 3.1 Pendulum example
00:55:12 4 See also



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SUMMARY
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In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.
The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a vector within that space.
To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
The state-space method is characterized by significant algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it.         
The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With 
  
    
      
        p
      
    
    {\displaystyle p}
   inputs and 
  
    
      
        q
      
    
    {\displaystyle q}
   outputs, we would otherwise have to write down 
  
    
      
        q
        ×
        p
      
    
    {\displaystyle q\times p}
   Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions. The state-space model is used in many different areas. In econometrics, the state-space model can be used for forecasting stock prices and numerous other variables.