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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. 

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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 ...
 
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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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Fri, 05 Dec 2014 01:22:30 -0800

1, the state's variable tax for conventional motor fuels will drop about a penny per gallon from 15.2 cents per gallon to 14.1 cents per gallon. The decrease is coming as a result of the state's annual tax recalculation, the Associated Press reported.
 
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Mon, 01 Dec 2014 09:15:00 -0800

1, the state's variable tax for conventional motor fuels will drop about a penny per gallon from 15.2 cents per gallon to 14.1 cents per gallon. The decrease will save motorists more than $15 million compared to what they are paying this year, Deputy ...
 
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The PEQ's four EQ sections use NE5532 dual op-amps in a state-variable filter topology. The SVF design has the advantage of allowing easy and simultaneous adjustment of Q and frequency in each section without interaction. The HP and LP filters use ...

ElectronicsWeekly.com

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Wed, 26 Nov 2014 21:40:11 -0800

It is the year 2004. With record high prices at the gas pumps and what seemed like a largely oil-explored world, it was an occasion to do what engineers do best: identify technical problems and devise solutions. With what seemed like a real “peak oil ...
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