State variable

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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.

Contents 1 Control Systems Engineering 1.1 Discrete-Time Systems 1.2 Continuous Time Systems (Analog) 2 See also

[edit] 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:

existing in dimension R^N*N

existing in dimension R^N*L

existing in dimension R^M*N

existing in dimension R^M*L

[edit] Discrete-Time Systems

The state variable representing the current state of a discrete-time system (i.e. digital systems) is , where n is the discrete point at which the system is being evaluated. The discrete-time state equations are

, which describes the next state of the system (x(n+1)) with respect to current state and inputs u(n) of the system.

, which describes the output Y(n) with respect to current states and inputs u(n) to the system.

[edit] Continuous Time Systems (Analog)

The state variable representing the current state of a continuous-time system (i.e. analog systems) is , 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.

, which describes the output Y(t) with respect to current states x(t) and inputs u(t) to the system.

[edit] See also

• State space (controls)
• Control theory
• Equation of state
• State (computer science)
• State (physics)
• State (functional analysis)
• State diagram
• State variable filter

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