Health Dictionary
Reliable, easy-to-read patient information on common medical conditions — written in plain language, free of jargon, and grounded in current evidence. Browse the most frequent diagnoses, understand what they mean for everyday life, and learn which steps and questions help you have a focused conversation with your doctor.
State variable
Introduction
A state variable is an element of the set of variables that describe the state of a dynamical system.
In case of simple mechanical systems, position coordinates and their derivates are typical state variables. Temperature, pressure, internal energy, enthalpy, entropy are examples of state variables in a thermodynamics system.
Control Systems Engineering
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:
<math>A\,\!</math> existing in dimension RN*N
<math>B\,\!</math> existing in dimension RN*L
<math>C\,\!</math> existing in dimension RM*N
<math>D\,\!</math> existing in dimension RM*L
Discrete-Time Systems
The state variable representing the current state of a discrete-time system (i.e. digital systems) is <math>x(n)\,</math>, where n is the discrete point at which the system is being evaluated. The discrete-time state equations are
- <math> x(n+1) = Ax(n) + Bu(n)\,\!</math> , which describes the next state of the system (x(n+1)) with respect to current state and inputs u(n) of the system.
- <math> Y(n) = Cx(n) + Du(n)\,\!</math> , 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 <math>x(t)\,</math>, and the continuous time state equations are
- <math> \frac{dx(t)}{dt} \ = Ax(t) + Bu(t)\,\!</math> , which describes the next state of the system <math> \frac{dx(t)}{dt} \,\!</math> with respect to current state x(t) and inputs u(t) of the system.
- <math> Y(t) = Cx(t) + Du(t)\,\!</math> , which describes the output Y(t) with respect to current states x(t) and inputs u(t) to the system.