- State variable
A state variable is an element of the set of variables that describe the state of a
In case of simple mechanical systems, position coordinates and their derivates are typical state variables.
Temperature, pressure, internal energy, enthalpy, entropyare examples of state variables in a thermodynamics system.
Control Systems Engineering
Control Engineeringand 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 invariantsystem 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"
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.
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.
State space (controls)
Equation of state
State (computer science)
State (functional analysis)
State variable filter
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