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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 a 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...  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...  State Space Representation ( Dynamic Systems )  Mechanical Engineering State Space Representation Dynamic Systems.  Proof: S (or Entropy) is a valid state variable More free lessons at: http://www.khanacademy.org/video?v=sPz5RrFus1Q Prroof that S (or entropy) is a valid state variable.  Lecture  46 StateVariable Methods(2) 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...  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...  SVF201 Analogue State Variable Filter Module The KOMA Elektronik SVF201 is a state variable filter for the Eurorack modular synthesizer system. Its filter circuit is built up with optical parts (Vactro...  Synthesizers.com Q107 State Variable Filter Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter.  Intellijel  uVCF State Variable FIlter demo General overview of the uVCF filter including the LowPass, Bandpass and Highpass outputs, sine VCO functionality and FM.  Tasker 101 Tutorials: Lesson 16b  Screen State Variable, SIMPLE Lock Screen, Addnl Lock Options In this lesson we build on Lesson 16a, adding the option to have the screen turn back on IF it was originally on when you connected to Wifi or Bluetooth and ... 

StateImpact Oklahoma
Thu, 24 Apr 2014 04:46:06 0700
And now, the state's variable climate is helping scientists understand how climate change could affect farms everywhere. The federal government recently picked an agricultural laboratory in El Reno to be one of seven regional hubs to study climate change.
 Premier Guitar 
Premier Guitar
Sun, 20 Apr 2014 05:33:45 0700
Among the pedal's coolest features is its threeposition statevariable filter switch, which works in tandem with the preEQ control to set the hipass, lowpass, or bandpass frequency. A postEQ knob sets the amount of upper harmonics in the ...
 
Design News
Fri, 18 Apr 2014 02:33:45 0700
The statevariable equations (see diagram above) are a coupled set of firstorder, ordinary, differential equations where the derivative of each state variable is expressed as an algebraic function of state variables, inputs, and possibly time. The ...
 
Dr. Dobb's
Mon, 07 Apr 2014 08:11:14 0700
You can set up one hot encoding, gray code encoding, outputs that are stored instead of derived from the state variable, and different types of outputs. There is a way to insert arbitrary code into the output, and a way to pass constraints to do things ...
 
Wall Street Journal (blog)
Wed, 16 Apr 2014 05:49:32 0700
“Bulges in their enrollments appear to be highly persistent,” Mr. Hall wrote. “Both programs place high taxes on earnings and so discourage laborforce participation among beneficiaries. The bulge in program dependence is a state variable arguably ...
 
PublicCEO.com
Thu, 10 Apr 2014 06:18:45 0700
California's native species have, through natural selection, adapted to the state's variable climate. However, these species are now attempting to survive in novel ecosystems, with highly altered hydrology and habitat often dominated by nonnative ...
 
Sonic State
Fri, 11 Apr 2014 06:41:15 0700
At Musikmesse this year we got a look at the range of modular pedals on offer from KOMA Elektronik. All the of their designs are pretty innovative and have some very cool features. The FT201 is a state variable voltage controlled vactrol analog filter ...
 
MNI News
Sat, 12 Apr 2014 08:33:45 0700
Hall's paper says it is unambiguous the capital stock is "an important state variable of the economy." The paper concludes it is responsible for the largest part of the output shortfall, 5.0 percentage points. "A boost would probably trigger an ...

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