Tracking Control of Linear Systems

Chapter 10 Linear tracking control (LITC)

10.1 Generating theorem

The book [148] contains what follows.

A complex valued matrix function F(.) : ℭ → ℭ^p×n is real rational matrix function if, and only if, it becomes a real valued matrix for the real value of the complex variable s, i.e., for s = σ ∊ ℜ, and every entry of F(s) is a quotient of two polynomials in s.

Let F(s) have µ different poles denoted by $s_k^{*}$, k = 1, 2, … µ. The multiplicity of the pole $s_k^{*}$ is designated by V_k. We denote its real and imaginary part by Re $s_k^{*}$ and Im $s_k^{*}$, respectively.

Theorem 304 Generating theorem

Let F(.) : ℜ → ℜ^p×n, F(t) = [F_ij(t)] , have Laplace transform F(.) : ℭ → ℜ^p×n, F(s) = [F_įj (s)] , that is real rational matrix function. In order for the norm ||