# Difference between revisions of "Dictionary:State variable"

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One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation: | One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation: | ||

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<center><math> E(t)=RI + L\frac{dI}{dt} +C\int_t I dt</math>. </center> | <center><math> E(t)=RI + L\frac{dI}{dt} +C\int_t I dt</math>. </center> | ||

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Using state variables of <math display="inline">I </math>, <math display="inline">Q=\int I dt </math>, and <math display="inline">P=\frac{dI}{dt}</math> permits this to be written as a set of three simultaneous equations: | Using state variables of <math display="inline">I </math>, <math display="inline">Q=\int I dt </math>, and <math display="inline">P=\frac{dI}{dt}</math> permits this to be written as a set of three simultaneous equations: | ||

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<center><math>E(t)=RI+LP+CQ </math>, | <center><math>E(t)=RI+LP+CQ </math>, | ||

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<math>\frac{dQ}{dt}=I</math>, and | <math>\frac{dQ}{dt}=I</math>, and | ||

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<math>\frac{dI}{dt}=P </math>.</center> | <math>\frac{dI}{dt}=P </math>.</center> | ||

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See also [[Special:MyLanguage/Dictionary:parameter|''parameter'']]. | See also [[Special:MyLanguage/Dictionary:parameter|''parameter'']]. | ||

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## Latest revision as of 03:00, 28 January 2018

One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:

Using state variables of , , and permits this to be written as a set of three simultaneous equations:

, and

See also *parameter*.