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 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.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
419229 videos foundNext > 

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 diagram, ...

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 ...

Intro to Control - 6.1 State-Space Model Basics

Explanation of state-space modeling of systems for controls.

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.

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 ...

Manhattan Analog - State Variable VCF

Here's my overview video for the SVVCF (Stave Variable Voltage Controlled Filter) from Manhattan Analog. Check out the sound and patches in the video, feel ...

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

State variable form extra example 2nd order

419229 videos foundNext > 

144 news items

U.S. Naval Research Laboratory (press release)

U.S. Naval Research Laboratory (press release)
Tue, 23 Jun 2015 13:37:30 -0700

Including electron spin as an additional state variable offers new prospects for information processing, enabling future non-volatile, reprogrammable devices beyond the current semiconductor technology roadmap. Silicon is an ideal host for such a spin ...

Nanowerk

Nanowerk
Wed, 24 Jun 2015 05:33:45 -0700

Including electron spin as an additional state variable offers new prospects for information processing, enabling future non-volatile, reprogrammable devices beyond the current semiconductor technology roadmap. Silicon is an ideal host for such a spin ...
 
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 ...
 
Space Daily
Tue, 09 Jun 2015 08:00:00 -0700

The protocol uses pairs of photons that are "hyperentangled"--simultaneously entangled in more than one state variable, in this case in polarization and in orbital angular momentum--with a restricted number of possible states in each variable. In this ...

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 ...

GoPSUsports.com

GoPSUsports.com
Wed, 25 Feb 2015 11:16:27 -0800

Introduced last year by Penn State, variable pricing determines individual game prices from many factors, including the expected demand for that game, and provides more pricing choices for Nittany Lion fans. Season tickets, which are on sale for 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.
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