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.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
572469 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.

Proof: S (or Entropy) is a valid state variable

Prroof that S (or entropy) is a valid state variable. More free lessons at: http://www.khanacademy.org/video?v=sPz5RrFus1Q.

Introduction to State Space (State Variable) Representation

Develops, by example, the state variable representation of a 3rd order LTI system, beginning with it's scalar differential equation, creating a signal block ...

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...

Synthesizers.com Q107 State Variable Filter

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

GATE 2013 ECE State Variable Analysis control systems

Intellijel - uVCF State Variable FIlter demo

General overview of the uVCF filter including the LowPass, Bandpass and Highpass outputs, sine VCO functionality and FM.

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...

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...

572469 videos foundNext > 

4 news items

Rock Hill Herald (press release)

Rock Hill Herald (press release)
Wed, 15 Oct 2014 04:03:45 -0700

State estimation is the process of assigning a value to an unknown system state variable, based on measurements from that system based on preset criteria. The process involves imperfect measurements that are redundant and the process of estimating the ...
 
GameDev.net
Tue, 07 Oct 2014 08:23:55 -0700

I don't know much about Swift, but you can have a state variable (that can be START, PLAY, GAME_OVER) and in your update method you can check what the state is and respond differently. Like so: -(void)update { if (self.state == START) { if (button ...
 
GameDev.net
Tue, 30 Sep 2014 12:30:17 -0700

Dozens of questions need to be asked - is the problem an OpenGL state variable issue, a shader issue, a problem with your loaded models/textures, etc? Being able to quickly answer these questions would save me truckloads of time. I also think using a ...
 
GameDev.net
Sun, 05 Oct 2014 01:24:47 -0700

i think you're tracking two states (moving and attacking) with one state variable. as frob says, you can enumerate the combos as a single state variable, or use individual state variables, as described by sean: If you have completely independent ...
Loading

Oops, we seem to be having trouble contacting Twitter

Support Wikipedia

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

Searchlight Group

Digplanet also receives support from Searchlight Group. Visit Searchlight