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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 firstorder differential equations are said to be in statevariable form.^{[1]}
Examples[edit]
 In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system.
 In thermodynamics, a state variable is also called a state function. Examples include temperature, pressure, volume, internal energy, enthalpy, and entropy. In contrast heat and work are not state functions, but process functions.
 In electronic circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables.
 In ecosystem models, population sizes (or concentrations) of plants, animals and resources (nutrients, organic material) are typical state variables.
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:
 R^{N*N}, R^{N*L}, R^{M*N}, R^{M*L},
where N, L and M are the dimensions of the vectors describing the state, input and output, respectively.
Discretetime systems[edit]
The state variable representing the current state of a discretetime system (i.e. digital system) is , where n is the discrete point at which the system is being evaluated. The discretetime state equations are
 , which describes the next state of the system (x[n+1]) with respect to current state and inputs u[n] of the system.
 , 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 continuoustime system (i.e. analog system) is , and the continuous time state equations are
 , which describes the next state of the system with respect to current state x(t) and inputs u(t) of the system.
 , 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]
 ^ William J. Palm III (2010). System Dynamics (2nd ed.). p. 225.
https://youtube.com/devicesupport  Lecture  45 StateVariable 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.iitm.ac.in.  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, defining state variables,...  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.  GATE 2013 ECE State Variable Analysis control systems  Lec47 StateVariable 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.iitm.ac.in.  Tasker 101 Tutorials: Lesson 16b  Screen State Variable, SIMPLE Lock Screen, Addnl Lock Options Tasker 101 Tutorials: Lesson 16b  Screen State Variable, SIMPLE lockscreen, Addnl Lock Options In this lesson we build on Lesson 16a, adding the option to have the screen turn back on IF...  KONTOUR: 3  The State Variable Filter and the Comb Filter  Intellijel  uVCF State Variable FIlter demo General overview of the uVCF filter including the LowPass, Bandpass and Highpass outputs, sine VCO functionality and FM. 
ValueWalk 
ValueWalk
Tue, 21 Apr 2015 05:56:15 0700
News contains valuable conditioning information that captures timevarying investor concern over different aspects of the macroeconomy. We create separate news measures to approximate investor concern about consumption growth, inflation, and ...
 MusicRadar.com 
MusicRadar.com
Tue, 14 Apr 2015 03:31:09 0700
Filter and destroy! The Filter Box Complete attacks with a pair of highly tuned filters and analog signal crushing. The state variable Filter module provides creamy, voltage controlled low pass, high pass, band pass, and notch filters while the LPG ...
 Gizmag 
Gizmag
Sat, 11 Apr 2015 04:35:19 0700
Parva has eight voices, each of which sports three digitallycontrolled oscillators with independent level controls for sawtooth, triangle and PWM wave forms, with the maker promising accurate pitch and reliable tuning stability. A twopole state ...
 
EDN.com
Mon, 15 Dec 2014 00:42:27 0800
The usual schematic of a statevariable 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 ...
 
Sonic State
Thu, 16 Apr 2015 09:41:15 0700
The first filter is the Cinnamon, a state variable filter with some really great features adding a depth of sound that can go from smooth and creamy, to crunchy and harsh with the flick of a switch. Then there is a 2HP passive filter called propust ...
 TAPinto.net 
TAPinto.net
Sun, 12 Apr 2015 19:03:45 0700
“The work is part of a $12.8 million, federallyfunded project that will resurface I80 travel lanes, shoulders and ramps using a oneinch thick high performance overlay,” said he state. “Variable message signs are being utilized throughout the project ...
 
PR Newswire (press release)
Tue, 24 Mar 2015 07:03:31 0700
BOSTON, March 24, 2015 /PRNewswire/  John Hancock Retirement Plan Services (JH RPS) has hired Erik Whinery as regional vice president, responsible for sales and relationship development with financial representatives and plan consultants in John ...
 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 ...

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