STATE VARIABLE

A 'state variable' is any variable which represents the state of an object.
Thermodynamic variables are sometimes called ''state variables''.

Contents

Control Systems Engineering

Discrete-Time Systems

Continuous Time Systems (Analog)

See also

Control Systems Engineering

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 (controls) 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 are expressed with Coefficient matrices:
$A,!$ existing in dimension 'R'^{''N
★ N''}
$B,!$ existing in dimension 'R'^{''N
★ L''}
$C,!$ existing in dimension 'R'^{''M
★ N''}
$D,!$ existing in dimension 'R'^{''M
★ L''}

Discrete-Time Systems

The state variable representing the current state of a discrete-time system (i.e. digital systems) is $x(n),$, where n is the discrete point at which the system is being evaluated. The discrete-time state equations are
: $x(n+1)\; =\; Ax(n)\; +\; Bu(n),!$ , which describes the next state of the system (x(n+1)) with respect to current state and inputs u(n) of the system.
: $Y(n)\; =\; Cx(n)\; +\; Du(n),!$ , which describes the output Y(n) with respect to current states and inputs u(n) to the system.

Continuous Time Systems (Analog)

The state variable representing the current state of a continuous-time system (i.e. analog systems) is $x(t),$, 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.
: $Y(t)\; =\; Cx(t)\; +\; Du(t),!$ , which describes the output Y(t) with respect to current states x(t) and inputs u(t) to the system.

See also

★ State space (controls)

★ Control theory

★ Equation of state

★ State (computer science)

★ State (physics)

★ State (functional analysis)

★ State diagram

★ State variable filter