Linear systems and the principle of superposition

A number of the systems described in the remainder of this chapter are assumed to be linear with respect to time, i.e. their time-dependent properties can be described by linear differential equations. Such systems follow the principle of superposition. This property is such that if the individual output of a system is 

In Fig. 7.10 G(s) is the transfer function of a particular linear system. If, for an input 3 , an output y, is obtained, both being expressed in terms of the Laplace transform  

Similarly, if the behaviour of the components of the block diagram illustrated in Fig. 7.3 can be assumed to be linear, then the effects of load and manipulated variable on the process can be added using the principle of superposition. 

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