What is the effect of relative degree in control theory?

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The term of relative degree is used a lot in books of control systems. I need some explaining to understand the useful and effect of the relative degree on analysis and design the control system. For example the following transfer function:$$G(s)=\frac{s+1}{s^2+s+1}$$has a relative degree one, another example the relative degree two or more. I need to know why it is important and where I have to take the relative degree in account when I design a control system.

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