digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Business

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

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.
A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
412415 videos foundNext > 

Lecture - 45 State-Variable 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...

State Space Representation ( Dynamic Systems ) | Mechanical Engineering

State Space Representation Dynamic Systems.

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...

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 State-Variable 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...

Lec-47 State-Variable 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...

Lecture 47 State Variable Methods (3)

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...

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 ...

Synthesizers.com Q107 State Variable Filter

Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter.

SVF-201 Analogue State Variable Filter Module

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 (Vactro...

412415 videos foundNext > 

18 news items

 
Design News
Fri, 18 Apr 2014 02:33:45 -0700

The state-variable equations (see diagram above) are a coupled set of first-order, ordinary, differential equations where the derivative of each state variable is expressed as an algebraic function of state variables, inputs, and possibly time. The ...
 
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 labor-force participation among beneficiaries. The bulge in program dependence is a state variable arguably ...
 
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 ...
 
Android Headlines - Android News
Fri, 11 Apr 2014 08:45:00 -0700

... state: Ethernet Connected, action Load Image: parameter Max Width Or Height, Services flag for app context, action Set Timer (system timer) (KitKat+)), action MIDI Play, user guide, section on MIDI, action edit: search menu option, state Variable ...
 
PublicCEO.com
Thu, 10 Apr 2014 06:19:30 -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 non-native ...
 
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 ...

Football Study Hall (blog)

Football Study Hall (blog)
Fri, 21 Mar 2014 06:52:30 -0700

The model overall had an r squared of just .04 and only the in-state variable was close to statistical significance at the 95% confidence level (with a P-value of .06). This means that, for the sample and holding the other variables constant, recruits ...
Loading

Oops, we seem to be having trouble contacting Twitter

Talk About State variable

You can talk about State variable with people all over the world in our discussions.

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!