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The term "linear" means that the control action is linear i.e., it obeys the laws of Additivity and Homogeneity:
- Additivity: f(x + y) = f(x) + f(y).
- Homogeneity of degree 1: f(αx) = αf(x) for all α.
The term "quadratic" is added to imply a quadratic cost function, associated with the control action. A quadratic cost function is taken and the integral of the same is minimised to get the optimal control law. A quadratic cost function has the advantage of being greater than or equal to zero for all values of the control variable.
The term "regulator" simply means "controller". Since this is a feedback control law, it regulates the value of a control variable.
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