Formation Control of Multi-Agent Systems

Appendix CSystems Theory

C.1 Linear Systems

The following material can be found in 129, 130. Given a real function of time satisfying the condition

for some finite real , its Laplace transform is defined as

where (complex number) is called the Laplace variable.

Two important properties of the Laplace transform are

Roughly speaking, the above properties indicate that multiplication by in the Laplace domain is equivalent to the differential operator in the time domain (). Likewise, division by in the Laplace domain is equivalent to the integral operator in the time domain ().

Consider the single‐input/single‐output ...