Functional Unknown Input Observers: Further Results and Applications
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 ∈ ℝ1×(n − p) is a row matrix, W1 ∈ ℝp×l and W2 ∈ ℝ(n − p)×l are known constant matrices and the pair (A12,A22) is observable. Matrices L1 ∈ ℝq×p, L2 ∈ ℝq×(n − p), D ∈ ℝ1×q and N ∈ ℝq×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.
KeywordsExistence Condition Unknown Input Rank Matrix Unknown Input Observer Order Observer
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