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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 first-order differential equations are said to be in state-variable form.[1]

Examples[edit]

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:

A\in RN*N, \quad B\in RN*L, \quad C\in RM*N, \quad D\in RM*L,

where N, L and M are the dimensions of the vectors describing the state, input and output, respectively.

Discrete-time systems[edit]

The state variable representing the current state of a discrete-time system (i.e. digital system) is x[n]\,, where n is the discrete point at which the system is being evaluated. The discrete-time state equations are

 x[n+1] = Ax[n] + Bu[n]\,\! , which describes the next state of the system (x[n+1]) with respect to current state and inputs u[n] of the system.
 y[n]   = Cx[n] + Du[n]\,\! , 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 continuous-time system (i.e. analog system) is x(t)\,, and the continuous time state equations are

 \frac{dx(t)}{dt} \ = Ax(t) + Bu(t)\,\! , which describes the next state of the system  \frac{dx(t)}{dt} \,\! with respect to current state x(t) and inputs u(t) of the system.
 y(t)   = Cx(t) + Du(t)\,\! , 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]

  1. ^ William J. Palm III (2010). System Dynamics (2nd ed.). p. 225. 

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/State_variable — Please support Wikipedia.
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133 news items

 
EDN.com
Mon, 15 Dec 2014 00:42:27 -0800

The usual schematic of a state-variable 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 seven-percent, with a market value of seven-point-three 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 SVF-201 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 state-variable class-A parametric equalizer. This 500-series 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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