Functional Unknown Input Observers: Further Results and Applications

Introduction

In Section 4.4 of Chapter 4, the design of reduced-order scalar functional observers for linear systems with unknown inputs has been discussed. The existence conditions have been presented in Proposition 4.3. It has been shown that the design of scalar functional observers for linear systems with unknown inputs is related to solving the following three coupled matrix equations

NL₂ − L₁A₁₂ − L₂A₂₂ = 0, N is Hurwitz (5.1)

F₂ = DL₂ (5.2)

L₁W₁ + L₂W₂ = 0 (5.3)

where F₂ ∈ ℝ^{1×(n − p)} is a row matrix, W₁ ∈ ℝ^p×l and W₂ ∈ ℝ^{(n − p)×l} are known constant matrices and the pair (A₁₂,A₂₂) is observable. Matrices L₁ ∈ ℝ^q×p, L₂ ∈ ℝ^{q×(n − p)}, D ∈ ℝ^1×q and N ∈ ℝ^q×q (N must be a stable matrix) are unknown. A solution method based on the parametric approach has been presented in Chapter 4 for solving the above three coupled matrix equations.