CSB −System

Linear CSB

Generalizing the basic CSB-system, with one input and one output (Figure 3.1), and including the principle of superposition for the system inputs and outputs, we come to the R.E. Kalman’s [Kal60] modular concept of linear multivariable system (Figure 5.1)

$$ \dot{x}=Ax+Bu,\qquad y=Cx,\qquad u=Dy $$

with the space of input signals (stimuli, excitations) U = {u}, state space $X=\{x,\dot{x}\}$ and space of output signals (reactions, responses) Y = {y}. (A linear, or vector, space is an ordered set whose elements can be added to each other, previously multiplied by a constant.)