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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 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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6399 news items

Avenue Mail

The Hindu
Thu, 04 Feb 2016 16:20:38 -0800

The chickpea variety, NBeG 47, is the first machine harvestable variety released in Andhra Pradesh suitable for the State's variable climate. This development was demonstrated recently in Anantapur district of Andhra Pradesh, showing how time and money ...

MusicRadar.com

MusicRadar.com
Thu, 21 Jan 2016 12:48:45 -0800

The architecture features two oscillators per voice, with continuously variable waveshapes (sawtooth and variable-width pulse, with triangle on oscillator 2). Each voice also has access to a SEM-inspired state-variable filter (low-pass, high-pass, band ...

The Hans India

The Hans India
Fri, 05 Feb 2016 20:01:59 -0800

The chickpea variety, NBeG 47, is the first machine harvestable variety released in Andhra Pradesh suitable for the state's variable climate. This development was demonstrated recently in a farmer's fields in Andhra Pradesh's Anantapur district showing ...
 
fnbnews.com
Sun, 07 Feb 2016 18:48:45 -0800

A 2.25 tonne of chickpea variety is harvested in just 75 minutes, instead of three long days that the process (including cutting and threshing) would take normally. This is made possible due to the breeding of a taller chickpea variety that is able to ...
 
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 ...

YouTube

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 ...

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 ...

SonicScoop

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.
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