A Parametric Approach to the Design of Reduced-Order Linear Functional Observers

Introduction

In Chapter 3, the design of linear functional observers of the form (3.6)-(3.7) has been discussed. It has been shown in Chapter 3 that the design of linear functional observers is related to solving the following reduced-order, coupled matrix equations

NL₂ − L₁A₁₂ − L₂A₂₂ = 0 (4.1)

F₂ = DL₂ (4.2)

where F₂ ∈ ℝ^{r×(n − p)} is a known full-row rank matrix and the pair (A₁₂,A₂₂) is observable. Matrices L₁ ∈ ℝ^q×p, L₂ ∈ ℝ^{q×(n − p)}, D ∈ ℝ^r×q and N ∈ ℝ^q×q (N must be a stable matrix) are unknown and need to be determined to satisfy (4.1)-(4.2).