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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. 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.
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 http://nptel.ii...  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 ...  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.  Lecture 48 State Variable Methods (4) Lecture Series on Networks and Systems by Prof.V.G.K.Murti, Department of Electrical Engineering, IIT Madras. For More details on NPTEL visit http://nptel.ii...  GATE 2013 ECE State Variable Analysis control systems  ECE 201 Lesson 25. How to solve for state variables in RL and RC circuits with step function inputs. The lesson develops a useful equation to solve for capacitor voltage in RC circuits and inductor currents in RL circuits with step function inputs. The role ...  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 http://nptel.iit...  Intellijel  uVCF State Variable FIlter demo General overview of the uVCF filter including the LowPass, Bandpass and Highpass outputs, sine VCO functionality and FM.  Q107 State Variable Filter module demo I've owned the Synthesizers.com Q107 since I obtained my first small set of modules. Since then I've obtained many other filters and have somewhat neglected ...  Synthesizers.com Q107 State Variable Filter Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter. 

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 ...
 
Pierce County Herald
Fri, 16 Jan 2015 13:31:36 0800
The state's Variable Fund has higher possible rewards and risks. Its preliminary return was sevenpercent, with a market value of sevenpointthree billion dollars. Final rates for the pension hikes have not been set. Changes in the retirees' checks ...
 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 ...
 
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.
 West Virginia Public Broadcasting 
Charleston Daily Mail
Sun, 30 Nov 2014 16:10:26 0800
The state's variable component for 2015 is 14.1 cents per gallon, a decrease compared to last year's 15.2 cents per gallon. The decrease will save West Virginia drivers $15.7 million in 2015 compared to what they paid this year, says Deputy Revenue ...
 
WKYT
Wed, 19 Nov 2014 08:18:45 0800
By virtue of the October 2014 survey, the state variable excise tax will decline by 4.3 cents per gallon on Jan. 1, 2014  to 21.2 cents per gallon from 25.5 cents. When the supplemental tax of 5 cents and underground petroleum tank fee of 1.4 cents ...
 
Network World
Mon, 15 Dec 2014 11:45:12 0800
The SDK also provides access to SysDB, a database that contains all state, variable, and other information for network processes. I've talked to some Arista customers that look at the SysDB database as the single best feature of EOS. Virtual EOS (vEOS).

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