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A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled firstorder differential equations are said to be in statevariable form.^{[1]}
Examples[edit]
 In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system.
 In thermodynamics, a state variable is also called a state function. Examples include temperature, pressure, volume, internal energy, enthalpy, and entropy. In contrast heat and work are not state functions, but process functions.
 In electronic circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables.
 In ecosystem models, population sizes (or concentrations) of plants, animals and resources (nutrients, organic material) are typical state variables.
Control systems engineering[edit]
In control engineering and other areas of science and engineering, state variables are used to represent the states of a general system. The state variables can be used to describe the state space of the system. The equations relating the current state and output of a system to its current input and past states are called the state equations. The state equations for a linear time invariant system can be expressed using coefficient matrices:
 R^{N*N}, R^{N*L}, R^{M*N}, R^{M*L},
where N, L and M are the dimensions of the vectors describing the state, input and output, respectively.
Discretetime systems[edit]
The state variable representing the current state of a discretetime system (i.e. digital system) is , where n is the discrete point at which the system is being evaluated. The discretetime state equations are
 , which describes the next state of the system (x[n+1]) with respect to current state and inputs u[n] of the system.
 , which describes the output y[n] with respect to current states and inputs u[n] to the system.
Continuous time systems[edit]
The state variable representing the current state of a continuoustime system (i.e. analog system) is , and the continuous time state equations are
 , which describes the next state of the system with respect to current state x(t) and inputs u(t) of the system.
 , which describes the output y(t) with respect to current states x(t) and inputs u(t) to the system.
See also[edit]
References[edit]
 ^ William J. Palm III (2010). System Dynamics (2nd ed.). p. 225.
Introduction to State Space (State Variable) Representation Develops, by example, the state variable representation of a 3rd order LTI system, beginning with it's scalar differential equation, creating a signal block diagram, ...  Lecture  45 StateVariable Methods (1) Lecture Series on Networks and Systems by Prof.V.G.K.Murti, Department of Electrical Engineering, IIT Madras. For More details on NPTEL visit ...  Intro to Control  6.1 StateSpace Model Basics Explanation of statespace modeling of systems for controls.  State Space Representation ( Dynamic Systems )  Mechanical Engineering State Space Representation Dynamic Systems.  Proof: S (or Entropy) is a valid state variable Prroof that S (or entropy) is a valid state variable. More free lessons at: http://www.khanacademy.org/video?v=sPz5RrFus1Q.  Lec47 StateVariable Equations Lecture Series on Control Engineering by Prof. S.D. Agashe, Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit ...  Manhattan Analog  State Variable VCF Here's my overview video for the SVVCF (Stave Variable Voltage Controlled Filter) from Manhattan Analog. Check out the sound and patches in the video, feel ...  Synthesizers.com Q107 State Variable Filter Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter.  GATE 2013 ECE State Variable Analysis control systems  State variable form extra example 2nd order 
U.S. Naval Research Laboratory (press release) 
U.S. Naval Research Laboratory (press release)
Tue, 23 Jun 2015 13:37:30 0700
Including electron spin as an additional state variable offers new prospects for information processing, enabling future nonvolatile, reprogrammable devices beyond the current semiconductor technology roadmap. Silicon is an ideal host for such a spin ...
 Nanowerk 
Nanowerk
Wed, 24 Jun 2015 05:33:45 0700
Including electron spin as an additional state variable offers new prospects for information processing, enabling future nonvolatile, reprogrammable devices beyond the current semiconductor technology roadmap. Silicon is an ideal host for such a spin ...
 
EDN.com
Mon, 15 Dec 2014 00:42:27 0800
The usual schematic of a statevariable filter with two inverting integrators is well known. Curiously, the input signal is almost always connected to the minus input of U1. Figure 1 is an example with ω0 = 1kHz and Q = 5. Figure 1 Typical state ...
 
Space Daily
Tue, 09 Jun 2015 08:00:00 0700
The protocol uses pairs of photons that are "hyperentangled"simultaneously entangled in more than one state variable, in this case in polarization and in orbital angular momentumwith a restricted number of possible states in each variable. In this ...
 GoPSUsports.com 
GoPSUsports.com
Tue, 14 Jan 2014 12:08:49 0800
UNIVERSITY PARK, Pa.  Penn State Athletics today announced variable pricing structure for its single game public football tickets during the 2014 season. Variable pricing determines individual game prices from many factors including expected demand ...
 
YouTube
Fri, 12 Oct 2012 06:00:07 0700
The KOMA Elektronik SVF201 is a state variable filter for the Eurorack modular synthesizer system. Its filter circuit is built up with optical parts (Vactrols) therefore delivering excellent studio audio quality and an unique warm analogue sound. The ...
 GoPSUsports.com 
GoPSUsports.com
Wed, 25 Feb 2015 11:16:27 0800
Introduced last year by Penn State, variable pricing determines individual game prices from many factors, including the expected demand for that game, and provides more pricing choices for Nittany Lion fans. Season tickets, which are on sale for the ...
 
SonicScoop
Wed, 03 Oct 2012 04:26:15 0700
In introducing their new Q4, Radial has debuted what they say “could very well be the world's first” 100% discrete statevariable classA parametric equalizer. This 500series module appears to be an enticing mix of classic engineering and new design.

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