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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.
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.ii...  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 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 Prroof that S (or entropy) is a valid state variable. More free lessons at: http://www.khanacademy.org/video?v=sPz5RrFus1Q.  Lecture  46 StateVariable 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...  Intellijel  uVCF State Variable FIlter demo General overview of the uVCF filter including the LowPass, Bandpass and Highpass outputs, sine VCO functionality and FM.  Synthesizers.com Q107 State Variable Filter Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter.  Lecture  49 State Variable Methods (5) 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...  GATE 2013 ECE State Variable Analysis control systems  Inigo Kennedy  State Variable [B] Automation Makers Art [1996] 

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 ...
 
Network World
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).
 
Insurance News Net
Mon, 15 Dec 2014 05:52:30 0800
Products may not be available in all states and product features may vary by state. Variable universal life insurance policies issued by AGL are distributed by AIG Capital Services, Inc. , member FINRA. Policy Form Numbers 14904, ICC1414904; Rider ...
 
Bluefield Daily Telegraph
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.
 
Huntington Herald Dispatch
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 ...
 
MIX
Fri, 05 Dec 2014 22:01:22 0800
The PEQ's four EQ sections use NE5532 dual opamps in a statevariable 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 
ElectronicsWeekly.com
Mon, 01 Dec 2014 02:16:51 0800
When your FPGA design fails to meet timing performance objectives, the cause may not be obvious. The solution lies not only in the FPGA implementation tools' talent in optimising the design to meet timing, but also in the designer's ability to specify ...
 
EDN.com (blog)
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 oilexplored 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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