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through components in the circuit are usually the state variables. In any electrical circuit, the number of state variables are equal to the number of (independent) storage elements, which are inductors and capacitors. The state variable for an inductor is the current through the inductor, while that
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of the system. The equations relating the current state of a system to its most recent input and past states are called the state equations, and the equations expressing the values of the output variables in terms of the state variables and inputs are called the output equations. As shown below, the
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144:. 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
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and other areas of science and engineering, state variables are used to represent the states of a general system. The set of possible combinations of state variable values is called the
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404:{\displaystyle A\in \mathbb {R} ^{N\times N},\quad B\in \mathbb {R} ^{N\times L},\quad C\in \mathbb {R} ^{M\times N},\quad D\in \mathbb {R} ^{M\times L},}
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of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system.
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is the discrete point in time at which the system is being evaluated. The discrete-time state equations are
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are the dimensions of the vectors describing the state, input and output, respectively.
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The state vector (vector of state variables) representing the current state of a
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Quantity used to describe the mathematical state of a dynamical system
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1008:(2nd ed.). McGraw-Hill Medical Publishing. p. 420.
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of the state of the system with respect to current state
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that are used to describe the mathematical "state" of a
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The state vector representing the current state of a
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for a capacitor is the voltage across the capacitor.
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763:{\displaystyle {\frac {dx(t)}{dt}}=Ax(t)+Bu(t),}
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120:Learn how and when to remove this message
559:of the system. The output equations are
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148:are said to be in state-variable form.
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58:adding citations to reliable sources
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917:) with respect to current states
899:{\displaystyle y(t)=Cx(t)+Du(t),}
949:Control (optimal control theory)
812:{\textstyle {\frac {dx(t)}{dt}}}
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1004:Palm, III William J. (2009).
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54:improve this article
250:control engineering
221:electrical circuits
176:. Examples include
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110:December 2009
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71: –
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65:Find sources:
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43:This article
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52:Please help
47:verification
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254:state space
186:temperature
991:References
217:electronic
163:velocities
80:newspapers
391:×
378:∈
363:×
350:∈
335:×
322:∈
307:×
294:∈
138:variables
1030:Category
937:See also
467:, where
263:matrices
229:currents
225:voltages
190:pressure
182:enthalpy
152:Examples
198:entropy
94:scholar
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414:where
277:, and
223:, the
194:volume
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101:JSTOR
87:books
1010:ISBN
422:and
206:work
204:and
202:Heat
196:and
73:news
248:In
235:In
215:In
168:In
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56:by
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219:/
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