Tracking Control of Linear Systems

Chapter 4 Transfer function matrix G (s)

4.1 On definitions of G (s)

There exist two approaches to define the system transfer function G (s) of the SISO system and its generalization, the transfer function matrix G (s) of the MIMO system. Laplace transform with its properties is the basis for both. Its application to derivatives of a (scalar or vector, either input or output) variable introduces the initial conditions (of the variable and of its derivatives) in the complex domain. Since system (scalar or matrix) parameters multiply the variable and its derivatives, therefore, the same parameters multiply the corresponding Laplace transforms of the variable and of its derivatives. The result is a sum of Laplace transform of the variable and ...