Tracking Control of Linear Systems

Chapter 7 Full transfer function matrix F (s)

7.1 General definitions of F(S)

This section develops further the concept of the system full transfer function matrix introduced in [81]. The general definitions presented in the sequel are equivalent to those in [148].

7.1.1 Definition of F(s): IO system

The full transfer function matrix F_IO (s) of the IO system (2.9) (Section 2.1), repeated as

$A^{(\nu )}{Y}^{\nu }(t)=B^{(\mu )}{I}^{\mu }(t),t\in 𝔗,$ (7.1)

describes in the complex domain ℭ how the system temporally transfers a simultaneous influence of an arbitrary input vector I (t), of any input initial conditions $I_{\text{0}\mp }, I_{\text{0}\mp }^{(1)}, \mathrm{...}, I_{\text{0}\mp }^{(\mu -1)}$ and of arbitrary output initial conditions $Y_{\text{0}\mp }, Y_{\text{0}\mp }^{(1)}, \mathrm{...}, Y_{\text{0}\mp }^{(v-1)}$ on the system output response Y(t), Fig. 7.1 [148]. Int 𝔗₀ is