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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 in the absence of any external forces affecting the system.
A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example ...
The number is always two or more; usually it is not more than some dozen. Though the number of state variables is fixed by experiment, there remains choice of which of them to use for a particular convenient description; a given thermodynamic system may be alternatively identified by several different choices of the set of state variables.
Output variables’ values depend on the state variable values and may also depend on the input variable values. The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector.
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. [1] [2] Most modern equations of state are formulated in the Helmholtz free energy.
A state diagram for a door that can only be opened and closed. A state diagram is used in computer science and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times this is a reasonable abstraction.
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.
As normally defined, it is a function of 4 variables (,,,) = , ˙ (,,) where is the state variable and is the control variable with respect to that which we are extremizing. The associated conditions for a maximum are